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Rechnet man das Additionsverfahren allgemein durch, erhält man eine fertige ",[1128,1129,1130],"strong",{},"Lösungsformel",". Beide Brüche haben denselben Nenner ",[568,1133,1135,1179],{"className":1134},[575],[568,1136,1138],{"className":1137},[579],[581,1139,1140],{"xmlns":583},[586,1141,1142,1176],{},[606,1143,1144,1147,1149,1155,1161,1164,1170],{},[612,1145,1146],{},"D",[623,1148,646],{},[609,1150,1151,1153],{},[612,1152,614],{},[616,1154,618],{},[609,1156,1157,1159],{},[612,1158,630],{},[616,1160,668],{},[623,1162,1163],{},"−",[609,1165,1166,1168],{},[612,1167,614],{},[616,1169,668],{},[609,1171,1172,1174],{},[612,1173,630],{},[616,1175,618],{},[698,1177,1178],{"encoding":700},"D = a_1 b_2 - a_2 b_1",[568,1180,1182,1202,1298],{"className":1181,"ariaHidden":604},[705],[568,1183,1185,1189,1193,1196,1199],{"className":1184},[709],[568,1186],{"className":1187,"style":1188},[713],"height:0.6833em;",[568,1190,1146],{"className":1191,"style":1192},[718,757],"margin-right:0.0278em;",[568,1194],{"className":1195,"style":1005},[809],[568,1197,646],{"className":1198},[1009],[568,1200],{"className":1201,"style":1005},[809],[568,1203,1205,1209,1249,1289,1292,1295],{"className":1204},[709],[568,1206],{"className":1207,"style":1208},[713],"height:0.8444em;vertical-align:-0.15em;",[568,1210,1212,1215],{"className":1211},[718],[568,1213,614],{"className":1214},[718,757],[568,1216,1218],{"className":1217},[761],[568,1219,1221,1241],{"className":1220},[729,730],[568,1222,1224,1238],{"className":1223},[734],[568,1225,1227],{"className":1226,"style":771},[738],[568,1228,1229,1232],{"style":774},[568,1230],{"className":1231,"style":778},[746],[568,1233,1235],{"className":1234},[782,783,784,785],[568,1236,618],{"className":1237},[718,785],[568,1239,793],{"className":1240},[792],[568,1242,1244],{"className":1243},[734],[568,1245,1247],{"className":1246,"style":800},[738],[568,1248],{},[568,1250,1252,1255],{"className":1251},[718],[568,1253,630],{"className":1254},[718,757],[568,1256,1258],{"className":1257},[761],[568,1259,1261,1281],{"className":1260},[729,730],[568,1262,1264,1278],{"className":1263},[734],[568,1265,1267],{"className":1266,"style":771},[738],[568,1268,1269,1272],{"style":774},[568,1270],{"className":1271,"style":778},[746],[568,1273,1275],{"className":1274},[782,783,784,785],[568,1276,668],{"className":1277},[718,785],[568,1279,793],{"className":1280},[792],[568,1282,1284],{"className":1283},[734],[568,1285,1287],{"className":1286,"style":800},[738],[568,1288],{},[568,1290],{"className":1291,"style":810},[809],[568,1293,1163],{"className":1294},[814],[568,1296],{"className":1297,"style":810},[809],[568,1299,1301,1304,1344],{"className":1300},[709],[568,1302],{"className":1303,"style":1208},[713],[568,1305,1307,1310],{"className":1306},[718],[568,1308,614],{"className":1309},[718,757],[568,1311,1313],{"className":1312},[761],[568,1314,1316,1336],{"className":1315},[729,730],[568,1317,1319,1333],{"className":1318},[734],[568,1320,1322],{"className":1321,"style":771},[738],[568,1323,1324,1327],{"style":774},[568,1325],{"className":1326,"style":778},[746],[568,1328,1330],{"className":1329},[782,783,784,785],[568,1331,668],{"className":1332},[718,785],[568,1334,793],{"className":1335},[792],[568,1337,1339],{"className":1338},[734],[568,1340,1342],{"className":1341,"style":800},[738],[568,1343],{},[568,1345,1347,1350],{"className":1346},[718],[568,1348,630],{"className":1349},[718,757],[568,1351,1353],{"className":1352},[761],[568,1354,1356,1376],{"className":1355},[729,730],[568,1357,1359,1373],{"className":1358},[734],[568,1360,1362],{"className":1361,"style":771},[738],[568,1363,1364,1367],{"style":774},[568,1365],{"className":1366,"style":778},[746],[568,1368,1370],{"className":1369},[782,783,784,785],[568,1371,618],{"className":1372},[718,785],[568,1374,793],{"className":1375},[792],[568,1377,1379],{"className":1378},[734],[568,1380,1382],{"className":1381,"style":800},[738],[568,1383],{},". Er heißt ",[1128,1386,1387],{},"Determinante"," des Systems und entscheidet über die Lösbarkeit:",[1390,1391,1392,1491],"ul",{},[1393,1394,1395,1490],"li",{},[568,1396,1398,1418],{"className":1397},[575],[568,1399,1401],{"className":1400},[579],[581,1402,1403],{"xmlns":583},[586,1404,1405,1415],{},[606,1406,1407,1409,1413],{},[612,1408,1146],{},[623,1410,1412],{"mathvariant":1411},"normal","≠",[616,1414,603],{},[698,1416,1417],{"encoding":700},"D \\neq 0",[568,1419,1421,1480],{"className":1420,"ariaHidden":604},[705],[568,1422,1424,1428,1431,1434,1477],{"className":1423},[709],[568,1425],{"className":1426,"style":1427},[713],"height:0.8889em;vertical-align:-0.1944em;",[568,1429,1146],{"className":1430,"style":1192},[718,757],[568,1432],{"className":1433,"style":1005},[809],[568,1435,1437,1470,1474],{"className":1436},[1009],[568,1438,1440],{"className":1439},[1009],[568,1441,1444],{"className":1442},[718,1443],"vbox",[568,1445,1448],{"className":1446},[1447],"thinbox",[568,1449,1452,1455,1466],{"className":1450},[1451],"rlap",[568,1453],{"className":1454,"style":1427},[713],[568,1456,1459],{"className":1457},[1458],"inner",[568,1460,1462],{"className":1461},[718],[568,1463,1465],{"className":1464},[1009],"",[568,1467],{"className":1468},[1469],"fix",[568,1471],{"className":1472},[809,1473],"nobreak",[568,1475,646],{"className":1476},[1009],[568,1478],{"className":1479,"style":1005},[809],[568,1481,1483,1487],{"className":1482},[709],[568,1484],{"className":1485,"style":1486},[713],"height:0.6444em;",[568,1488,603],{"className":1489},[718],": genau eine Lösung, die Formel liefert sie.",[1393,1492,1493,1544],{},[568,1494,1496,1514],{"className":1495},[575],[568,1497,1499],{"className":1498},[579],[581,1500,1501],{"xmlns":583},[586,1502,1503,1511],{},[606,1504,1505,1507,1509],{},[612,1506,1146],{},[623,1508,646],{},[616,1510,603],{},[698,1512,1513],{"encoding":700},"D = 0",[568,1515,1517,1535],{"className":1516,"ariaHidden":604},[705],[568,1518,1520,1523,1526,1529,1532],{"className":1519},[709],[568,1521],{"className":1522,"style":1188},[713],[568,1524,1146],{"className":1525,"style":1192},[718,757],[568,1527],{"className":1528,"style":1005},[809],[568,1530,646],{"className":1531},[1009],[568,1533],{"className":1534,"style":1005},[809],[568,1536,1538,1541],{"className":1537},[709],[568,1539],{"className":1540,"style":1486},[713],[568,1542,603],{"className":1543},[718],": keine Lösung oder unendlich viele Lösungen. Die zugehörigen Geraden sind parallel oder fallen zusammen. Die Formel ist dann nicht anwendbar.",[564,1546,1547,1548,1577,1578,1606,1607,1735,1736,1860,1861,1606,1889,2013],{},"Merkhilfe: Im Zähler von ",[568,1549,1551,1564],{"className":1550},[575],[568,1552,1554],{"className":1553},[579],[581,1555,1556],{"xmlns":583},[586,1557,1558,1562],{},[606,1559,1560],{},[612,1561,621],{},[698,1563,621],{"encoding":700},[568,1565,1567],{"className":1566,"ariaHidden":604},[705],[568,1568,1570,1574],{"className":1569},[709],[568,1571],{"className":1572,"style":1573},[713],"height:0.4306em;",[568,1575,621],{"className":1576},[718,757]," ersetzt man in ",[568,1579,1581,1594],{"className":1580},[575],[568,1582,1584],{"className":1583},[579],[581,1585,1586],{"xmlns":583},[586,1587,1588,1592],{},[606,1589,1590],{},[612,1591,1146],{},[698,1593,1146],{"encoding":700},[568,1595,1597],{"className":1596,"ariaHidden":604},[705],[568,1598,1600,1603],{"className":1599},[709],[568,1601],{"className":1602,"style":1188},[713],[568,1604,1146],{"className":1605,"style":1192},[718,757]," die Zahlen ",[568,1608,1610,1637],{"className":1609},[575],[568,1611,1613],{"className":1612},[579],[581,1614,1615],{"xmlns":583},[586,1616,1617,1634],{},[606,1618,1619,1625,1628],{},[609,1620,1621,1623],{},[612,1622,614],{},[616,1624,618],{},[623,1626,1627],{"separator":604},",",[609,1629,1630,1632],{},[612,1631,614],{},[616,1633,668],{},[698,1635,1636],{"encoding":700},"a_1, a_2",[568,1638,1640],{"className":1639,"ariaHidden":604},[705],[568,1641,1643,1647,1687,1691,1695],{"className":1642},[709],[568,1644],{"className":1645,"style":1646},[713],"height:0.625em;vertical-align:-0.1944em;",[568,1648,1650,1653],{"className":1649},[718],[568,1651,614],{"className":1652},[718,757],[568,1654,1656],{"className":1655},[761],[568,1657,1659,1679],{"className":1658},[729,730],[568,1660,1662,1676],{"className":1661},[734],[568,1663,1665],{"className":1664,"style":771},[738],[568,1666,1667,1670],{"style":774},[568,1668],{"className":1669,"style":778},[746],[568,1671,1673],{"className":1672},[782,783,784,785],[568,1674,618],{"className":1675},[718,785],[568,1677,793],{"className":1678},[792],[568,1680,1682],{"className":1681},[734],[568,1683,1685],{"className":1684,"style":800},[738],[568,1686],{},[568,1688,1627],{"className":1689},[1690],"mpunct",[568,1692],{"className":1693,"style":1694},[809],"margin-right:0.1667em;",[568,1696,1698,1701],{"className":1697},[718],[568,1699,614],{"className":1700},[718,757],[568,1702,1704],{"className":1703},[761],[568,1705,1707,1727],{"className":1706},[729,730],[568,1708,1710,1724],{"className":1709},[734],[568,1711,1713],{"className":1712,"style":771},[738],[568,1714,1715,1718],{"style":774},[568,1716],{"className":1717,"style":778},[746],[568,1719,1721],{"className":1720},[782,783,784,785],[568,1722,668],{"className":1723},[718,785],[568,1725,793],{"className":1726},[792],[568,1728,1730],{"className":1729},[734],[568,1731,1733],{"className":1732,"style":800},[738],[568,1734],{}," durch ",[568,1737,1739,1765],{"className":1738},[575],[568,1740,1742],{"className":1741},[579],[581,1743,1744],{"xmlns":583},[586,1745,1746,1762],{},[606,1747,1748,1754,1756],{},[609,1749,1750,1752],{},[612,1751,651],{},[616,1753,618],{},[623,1755,1627],{"separator":604},[609,1757,1758,1760],{},[612,1759,651],{},[616,1761,668],{},[698,1763,1764],{"encoding":700},"c_1, c_2",[568,1766,1768],{"className":1767,"ariaHidden":604},[705],[568,1769,1771,1774,1814,1817,1820],{"className":1770},[709],[568,1772],{"className":1773,"style":1646},[713],[568,1775,1777,1780],{"className":1776},[718],[568,1778,651],{"className":1779},[718,757],[568,1781,1783],{"className":1782},[761],[568,1784,1786,1806],{"className":1785},[729,730],[568,1787,1789,1803],{"className":1788},[734],[568,1790,1792],{"className":1791,"style":771},[738],[568,1793,1794,1797],{"style":774},[568,1795],{"className":1796,"style":778},[746],[568,1798,1800],{"className":1799},[782,783,784,785],[568,1801,618],{"className":1802},[718,785],[568,1804,793],{"className":1805},[792],[568,1807,1809],{"className":1808},[734],[568,1810,1812],{"className":1811,"style":800},[738],[568,1813],{},[568,1815,1627],{"className":1816},[1690],[568,1818],{"className":1819,"style":1694},[809],[568,1821,1823,1826],{"className":1822},[718],[568,1824,651],{"className":1825},[718,757],[568,1827,1829],{"className":1828},[761],[568,1830,1832,1852],{"className":1831},[729,730],[568,1833,1835,1849],{"className":1834},[734],[568,1836,1838],{"className":1837,"style":771},[738],[568,1839,1840,1843],{"style":774},[568,1841],{"className":1842,"style":778},[746],[568,1844,1846],{"className":1845},[782,783,784,785],[568,1847,668],{"className":1848},[718,785],[568,1850,793],{"className":1851},[792],[568,1853,1855],{"className":1854},[734],[568,1856,1858],{"className":1857,"style":800},[738],[568,1859],{},", im Zähler von ",[568,1862,1864,1877],{"className":1863},[575],[568,1865,1867],{"className":1866},[579],[581,1868,1869],{"xmlns":583},[586,1870,1871,1875],{},[606,1872,1873],{},[612,1874,635],{},[698,1876,635],{"encoding":700},[568,1878,1880],{"className":1879,"ariaHidden":604},[705],[568,1881,1883,1886],{"className":1882},[709],[568,1884],{"className":1885,"style":1646},[713],[568,1887,635],{"className":1888,"style":861},[718,757],[568,1890,1892,1918],{"className":1891},[575],[568,1893,1895],{"className":1894},[579],[581,1896,1897],{"xmlns":583},[586,1898,1899,1915],{},[606,1900,1901,1907,1909],{},[609,1902,1903,1905],{},[612,1904,630],{},[616,1906,618],{},[623,1908,1627],{"separator":604},[609,1910,1911,1913],{},[612,1912,630],{},[616,1914,668],{},[698,1916,1917],{"encoding":700},"b_1, b_2",[568,1919,1921],{"className":1920,"ariaHidden":604},[705],[568,1922,1924,1927,1967,1970,1973],{"className":1923},[709],[568,1925],{"className":1926,"style":1427},[713],[568,1928,1930,1933],{"className":1929},[718],[568,1931,630],{"className":1932},[718,757],[568,1934,1936],{"className":1935},[761],[568,1937,1939,1959],{"className":1938},[729,730],[568,1940,1942,1956],{"className":1941},[734],[568,1943,1945],{"className":1944,"style":771},[738],[568,1946,1947,1950],{"style":774},[568,1948],{"className":1949,"style":778},[746],[568,1951,1953],{"className":1952},[782,783,784,785],[568,1954,618],{"className":1955},[718,785],[568,1957,793],{"className":1958},[792],[568,1960,1962],{"className":1961},[734],[568,1963,1965],{"className":1964,"style":800},[738],[568,1966],{},[568,1968,1627],{"className":1969},[1690],[568,1971],{"className":1972,"style":1694},[809],[568,1974,1976,1979],{"className":1975},[718],[568,1977,630],{"className":1978},[718,757],[568,1980,1982],{"className":1981},[761],[568,1983,1985,2005],{"className":1984},[729,730],[568,1986,1988,2002],{"className":1987},[734],[568,1989,1991],{"className":1990,"style":771},[738],[568,1992,1993,1996],{"style":774},[568,1994],{"className":1995,"style":778},[746],[568,1997,1999],{"className":1998},[782,783,784,785],[568,2000,668],{"className":2001},[718,785],[568,2003,793],{"className":2004},[792],[568,2006,2008],{"className":2007},[734],[568,2009,2011],{"className":2010,"style":800},[738],[568,2012],{},". Das ist die Cramersche Regel für zwei Unbekannte.",[559,2015,2017],{"id":2016},"beispiele","Beispiele",[568,2019,2021],{"className":2020},[571],[568,2022,2024,2100],{"className":2023},[575],[568,2025,2027],{"className":2026},[579],[581,2028,2029],{"xmlns":583,"display":584},[586,2030,2031,2097],{},[589,2032,2033,2065],{"rowspacing":591,"columnalign":592,"columnspacing":593},[595,2034,2035,2052],{},[598,2036,2037],{},[601,2038,2039],{"scriptlevel":603,"displaystyle":604},[606,2040,2041,2044,2046,2048,2050],{},[616,2042,2043],{},"3",[612,2045,621],{},[623,2047,625],{},[616,2049,668],{},[612,2051,635],{},[598,2053,2054],{},[601,2055,2056],{"scriptlevel":603,"displaystyle":604},[606,2057,2058,2060,2062],{},[606,2059],{},[623,2061,646],{},[616,2063,2064],{},"7",[595,2066,2067,2085],{},[598,2068,2069],{},[601,2070,2071],{"scriptlevel":603,"displaystyle":604},[606,2072,2073,2076,2078,2080,2083],{},[616,2074,2075],{},"4",[612,2077,621],{},[623,2079,625],{},[616,2081,2082],{},"5",[612,2084,635],{},[598,2086,2087],{},[601,2088,2089],{"scriptlevel":603,"displaystyle":604},[606,2090,2091,2093,2095],{},[606,2092],{},[623,2094,646],{},[616,2096,2064],{},[698,2098,2099],{"encoding":700},"\\begin{aligned} 3x + 2y &= 7 \\\\ 4x + 5y &= 7 \\end{aligned}",[568,2101,2103],{"className":2102,"ariaHidden":604},[705],[568,2104,2106,2109],{"className":2105},[709],[568,2107],{"className":2108,"style":714},[713],[568,2110,2112],{"className":2111},[718],[568,2113,2115,2196],{"className":2114},[589],[568,2116,2118],{"className":2117},[725],[568,2119,2121,2188],{"className":2120},[729,730],[568,2122,2124,2185],{"className":2123},[734],[568,2125,2127,2156],{"className":2126,"style":739},[738],[568,2128,2129,2132],{"style":742},[568,2130],{"className":2131,"style":747},[746],[568,2133,2135,2138,2141,2144,2147,2150,2153],{"className":2134},[718],[568,2136,2043],{"className":2137},[718],[568,2139,621],{"className":2140},[718,757],[568,2142],{"className":2143,"style":810},[809],[568,2145,625],{"className":2146},[814],[568,2148],{"className":2149,"style":810},[809],[568,2151,668],{"className":2152},[718],[568,2154,635],{"className":2155,"style":861},[718,757],[568,2157,2158,2161],{"style":864},[568,2159],{"className":2160,"style":747},[746],[568,2162,2164,2167,2170,2173,2176,2179,2182],{"className":2163},[718],[568,2165,2075],{"className":2166},[718],[568,2168,621],{"className":2169},[718,757],[568,2171],{"className":2172,"style":810},[809],[568,2174,625],{"className":2175},[814],[568,2177],{"className":2178,"style":810},[809],[568,2180,2082],{"className":2181},[718],[568,2183,635],{"className":2184,"style":861},[718,757],[568,2186,793],{"className":2187},[792],[568,2189,2191],{"className":2190},[734],[568,2192,2194],{"className":2193,"style":975},[738],[568,2195],{},[568,2197,2199],{"className":2198},[981],[568,2200,2202,2257],{"className":2201},[729,730],[568,2203,2205,2254],{"className":2204},[734],[568,2206,2208,2231],{"className":2207,"style":739},[738],[568,2209,2210,2213],{"style":742},[568,2211],{"className":2212,"style":747},[746],[568,2214,2216,2219,2222,2225,2228],{"className":2215},[718],[568,2217],{"className":2218},[718],[568,2220],{"className":2221,"style":1005},[809],[568,2223,646],{"className":2224},[1009],[568,2226],{"className":2227,"style":1005},[809],[568,2229,2064],{"className":2230},[718],[568,2232,2233,2236],{"style":864},[568,2234],{"className":2235,"style":747},[746],[568,2237,2239,2242,2245,2248,2251],{"className":2238},[718],[568,2240],{"className":2241},[718],[568,2243],{"className":2244,"style":1005},[809],[568,2246,646],{"className":2247},[1009],[568,2249],{"className":2250,"style":1005},[809],[568,2252,2064],{"className":2253},[718],[568,2255,793],{"className":2256},[792],[568,2258,2260],{"className":2259},[734],[568,2261,2263],{"className":2262,"style":975},[738],[568,2264],{},[564,2266,2267,2268,2409],{},"Determinante ",[568,2269,2271,2306],{"className":2270},[575],[568,2272,2274],{"className":2273},[579],[581,2275,2276],{"xmlns":583},[586,2277,2278,2303],{},[606,2279,2280,2282,2284,2286,2289,2291,2293,2295,2297,2299,2301],{},[612,2281,1146],{},[623,2283,646],{},[616,2285,2043],{},[623,2287,2288],{},"⋅",[616,2290,2082],{},[623,2292,1163],{},[616,2294,2075],{},[623,2296,2288],{},[616,2298,668],{},[623,2300,646],{},[616,2302,2064],{},[698,2304,2305],{"encoding":700},"D = 3 \\cdot 5 - 4 \\cdot 2 = 7",[568,2307,2309,2327,2345,2364,2382,2400],{"className":2308,"ariaHidden":604},[705],[568,2310,2312,2315,2318,2321,2324],{"className":2311},[709],[568,2313],{"className":2314,"style":1188},[713],[568,2316,1146],{"className":2317,"style":1192},[718,757],[568,2319],{"className":2320,"style":1005},[809],[568,2322,646],{"className":2323},[1009],[568,2325],{"className":2326,"style":1005},[809],[568,2328,2330,2333,2336,2339,2342],{"className":2329},[709],[568,2331],{"className":2332,"style":1486},[713],[568,2334,2043],{"className":2335},[718],[568,2337],{"className":2338,"style":810},[809],[568,2340,2288],{"className":2341},[814],[568,2343],{"className":2344,"style":810},[809],[568,2346,2348,2352,2355,2358,2361],{"className":2347},[709],[568,2349],{"className":2350,"style":2351},[713],"height:0.7278em;vertical-align:-0.0833em;",[568,2353,2082],{"className":2354},[718],[568,2356],{"className":2357,"style":810},[809],[568,2359,1163],{"className":2360},[814],[568,2362],{"className":2363,"style":810},[809],[568,2365,2367,2370,2373,2376,2379],{"className":2366},[709],[568,2368],{"className":2369,"style":1486},[713],[568,2371,2075],{"className":2372},[718],[568,2374],{"className":2375,"style":810},[809],[568,2377,2288],{"className":2378},[814],[568,2380],{"className":2381,"style":810},[809],[568,2383,2385,2388,2391,2394,2397],{"className":2384},[709],[568,2386],{"className":2387,"style":1486},[713],[568,2389,668],{"className":2390},[718],[568,2392],{"className":2393,"style":1005},[809],[568,2395,646],{"className":2396},[1009],[568,2398],{"className":2399,"style":1005},[809],[568,2401,2403,2406],{"className":2402},[709],[568,2404],{"className":2405,"style":1486},[713],[568,2407,2064],{"className":2408},[718],", also gibt es genau eine Lösung:",[568,2411,2413],{"className":2412},[571],[568,2414,2416,2513],{"className":2415},[575],[568,2417,2419],{"className":2418},[579],[581,2420,2421],{"xmlns":583,"display":584},[586,2422,2423,2510],{},[606,2424,2425,2427,2429,2450,2452,2459,2461,2463,2465,2468,2470,2472,2492,2494,2504,2506,2508],{},[612,2426,621],{},[623,2428,646],{},[2430,2431,2432,2448],"mfrac",{},[606,2433,2434,2436,2438,2440,2442,2444,2446],{},[616,2435,2064],{},[623,2437,2288],{},[616,2439,2082],{},[623,2441,1163],{},[616,2443,2064],{},[623,2445,2288],{},[616,2447,668],{},[616,2449,2064],{},[623,2451,646],{},[2430,2453,2454,2457],{},[616,2455,2456],{},"21",[616,2458,2064],{},[623,2460,646],{},[616,2462,2043],{},[623,2464,1627],{"separator":604},[809,2466],{"width":2467},"2em",[612,2469,635],{},[623,2471,646],{},[2430,2473,2474,2490],{},[606,2475,2476,2478,2480,2482,2484,2486,2488],{},[616,2477,2043],{},[623,2479,2288],{},[616,2481,2064],{},[623,2483,1163],{},[616,2485,2075],{},[623,2487,2288],{},[616,2489,2064],{},[616,2491,2064],{},[623,2493,646],{},[2430,2495,2496,2502],{},[606,2497,2498,2500],{},[623,2499,1163],{},[616,2501,2064],{},[616,2503,2064],{},[623,2505,646],{},[623,2507,1163],{},[616,2509,618],{},[698,2511,2512],{"encoding":700},"x = \\frac{7 \\cdot 5 - 7 \\cdot 2}{7} = \\frac{21}{7} = 3, \\qquad y = \\frac{3 \\cdot 7 - 4 \\cdot 7}{7} = \\frac{-7}{7} = -1",[568,2514,2516,2534,2658,2735,2767,2880,2960],{"className":2515,"ariaHidden":604},[705],[568,2517,2519,2522,2525,2528,2531],{"className":2518},[709],[568,2520],{"className":2521,"style":1573},[713],[568,2523,621],{"className":2524},[718,757],[568,2526],{"className":2527,"style":1005},[809],[568,2529,646],{"className":2530},[1009],[568,2532],{"className":2533,"style":1005},[809],[568,2535,2537,2541,2649,2652,2655],{"className":2536},[709],[568,2538],{"className":2539,"style":2540},[713],"height:2.0074em;vertical-align:-0.686em;",[568,2542,2544,2549,2645],{"className":2543},[718],[568,2545],{"className":2546},[2547,2548],"mopen","nulldelimiter",[568,2550,2552],{"className":2551},[2430],[568,2553,2555,2636],{"className":2554},[729,730],[568,2556,2558,2633],{"className":2557},[734],[568,2559,2562,2574,2585],{"className":2560,"style":2561},[738],"height:1.3214em;",[568,2563,2565,2568],{"style":2564},"top:-2.314em;",[568,2566],{"className":2567,"style":747},[746],[568,2569,2571],{"className":2570},[718],[568,2572,2064],{"className":2573},[718],[568,2575,2577,2580],{"style":2576},"top:-3.23em;",[568,2578],{"className":2579,"style":747},[746],[568,2581],{"className":2582,"style":2584},[2583],"frac-line","border-bottom-width:0.04em;",[568,2586,2588,2591],{"style":2587},"top:-3.677em;",[568,2589],{"className":2590,"style":747},[746],[568,2592,2594,2597,2600,2603,2606,2609,2612,2615,2618,2621,2624,2627,2630],{"className":2593},[718],[568,2595,2064],{"className":2596},[718],[568,2598],{"className":2599,"style":810},[809],[568,2601,2288],{"className":2602},[814],[568,2604],{"className":2605,"style":810},[809],[568,2607,2082],{"className":2608},[718],[568,2610],{"className":2611,"style":810},[809],[568,2613,1163],{"className":2614},[814],[568,2616],{"className":2617,"style":810},[809],[568,2619,2064],{"className":2620},[718],[568,2622],{"className":2623,"style":810},[809],[568,2625,2288],{"className":2626},[814],[568,2628],{"className":2629,"style":810},[809],[568,2631,668],{"className":2632},[718],[568,2634,793],{"className":2635},[792],[568,2637,2639],{"className":2638},[734],[568,2640,2643],{"className":2641,"style":2642},[738],"height:0.686em;",[568,2644],{},[568,2646],{"className":2647},[2648,2548],"mclose",[568,2650],{"className":2651,"style":1005},[809],[568,2653,646],{"className":2654},[1009],[568,2656],{"className":2657,"style":1005},[809],[568,2659,2661,2664,2726,2729,2732],{"className":2660},[709],[568,2662],{"className":2663,"style":2540},[713],[568,2665,2667,2670,2723],{"className":2666},[718],[568,2668],{"className":2669},[2547,2548],[568,2671,2673],{"className":2672},[2430],[568,2674,2676,2715],{"className":2675},[729,730],[568,2677,2679,2712],{"className":2678},[734],[568,2680,2682,2693,2701],{"className":2681,"style":2561},[738],[568,2683,2684,2687],{"style":2564},[568,2685],{"className":2686,"style":747},[746],[568,2688,2690],{"className":2689},[718],[568,2691,2064],{"className":2692},[718],[568,2694,2695,2698],{"style":2576},[568,2696],{"className":2697,"style":747},[746],[568,2699],{"className":2700,"style":2584},[2583],[568,2702,2703,2706],{"style":2587},[568,2704],{"className":2705,"style":747},[746],[568,2707,2709],{"className":2708},[718],[568,2710,2456],{"className":2711},[718],[568,2713,793],{"className":2714},[792],[568,2716,2718],{"className":2717},[734],[568,2719,2721],{"className":2720,"style":2642},[738],[568,2722],{},[568,2724],{"className":2725},[2648,2548],[568,2727],{"className":2728,"style":1005},[809],[568,2730,646],{"className":2731},[1009],[568,2733],{"className":2734,"style":1005},[809],[568,2736,2738,2742,2745,2748,2752,2755,2758,2761,2764],{"className":2737},[709],[568,2739],{"className":2740,"style":2741},[713],"height:0.8389em;vertical-align:-0.1944em;",[568,2743,2043],{"className":2744},[718],[568,2746,1627],{"className":2747},[1690],[568,2749],{"className":2750,"style":2751},[809],"margin-right:2em;",[568,2753],{"className":2754,"style":1694},[809],[568,2756,635],{"className":2757,"style":861},[718,757],[568,2759],{"className":2760,"style":1005},[809],[568,2762,646],{"className":2763},[1009],[568,2765],{"className":2766,"style":1005},[809],[568,2768,2770,2773,2871,2874,2877],{"className":2769},[709],[568,2771],{"className":2772,"style":2540},[713],[568,2774,2776,2779,2868],{"className":2775},[718],[568,2777],{"className":2778},[2547,2548],[568,2780,2782],{"className":2781},[2430],[568,2783,2785,2860],{"className":2784},[729,730],[568,2786,2788,2857],{"className":2787},[734],[568,2789,2791,2802,2810],{"className":2790,"style":2561},[738],[568,2792,2793,2796],{"style":2564},[568,2794],{"className":2795,"style":747},[746],[568,2797,2799],{"className":2798},[718],[568,2800,2064],{"className":2801},[718],[568,2803,2804,2807],{"style":2576},[568,2805],{"className":2806,"style":747},[746],[568,2808],{"className":2809,"style":2584},[2583],[568,2811,2812,2815],{"style":2587},[568,2813],{"className":2814,"style":747},[746],[568,2816,2818,2821,2824,2827,2830,2833,2836,2839,2842,2845,2848,2851,2854],{"className":2817},[718],[568,2819,2043],{"className":2820},[718],[568,2822],{"className":2823,"style":810},[809],[568,2825,2288],{"className":2826},[814],[568,2828],{"className":2829,"style":810},[809],[568,2831,2064],{"className":2832},[718],[568,2834],{"className":2835,"style":810},[809],[568,2837,1163],{"className":2838},[814],[568,2840],{"className":2841,"style":810},[809],[568,2843,2075],{"className":2844},[718],[568,2846],{"className":2847,"style":810},[809],[568,2849,2288],{"className":2850},[814],[568,2852],{"className":2853,"style":810},[809],[568,2855,2064],{"className":2856},[718],[568,2858,793],{"className":2859},[792],[568,2861,2863],{"className":2862},[734],[568,2864,2866],{"className":2865,"style":2642},[738],[568,2867],{},[568,2869],{"className":2870},[2648,2548],[568,2872],{"className":2873,"style":1005},[809],[568,2875,646],{"className":2876},[1009],[568,2878],{"className":2879,"style":1005},[809],[568,2881,2883,2886,2951,2954,2957],{"className":2882},[709],[568,2884],{"className":2885,"style":2540},[713],[568,2887,2889,2892,2948],{"className":2888},[718],[568,2890],{"className":2891},[2547,2548],[568,2893,2895],{"className":2894},[2430],[568,2896,2898,2940],{"className":2897},[729,730],[568,2899,2901,2937],{"className":2900},[734],[568,2902,2904,2915,2923],{"className":2903,"style":2561},[738],[568,2905,2906,2909],{"style":2564},[568,2907],{"className":2908,"style":747},[746],[568,2910,2912],{"className":2911},[718],[568,2913,2064],{"className":2914},[718],[568,2916,2917,2920],{"style":2576},[568,2918],{"className":2919,"style":747},[746],[568,2921],{"className":2922,"style":2584},[2583],[568,2924,2925,2928],{"style":2587},[568,2926],{"className":2927,"style":747},[746],[568,2929,2931,2934],{"className":2930},[718],[568,2932,1163],{"className":2933},[718],[568,2935,2064],{"className":2936},[718],[568,2938,793],{"className":2939},[792],[568,2941,2943],{"className":2942},[734],[568,2944,2946],{"className":2945,"style":2642},[738],[568,2947],{},[568,2949],{"className":2950},[2648,2548],[568,2952],{"className":2953,"style":1005},[809],[568,2955,646],{"className":2956},[1009],[568,2958],{"className":2959,"style":1005},[809],[568,2961,2963,2966,2969],{"className":2962},[709],[568,2964],{"className":2965,"style":2351},[713],[568,2967,1163],{"className":2968},[718],[568,2970,618],{"className":2971},[718],[564,2973,2974],{},"Mit negativen Koeffizienten:",[568,2976,2978],{"className":2977},[571],[568,2979,2981,3051],{"className":2980},[575],[568,2982,2984],{"className":2983},[579],[581,2985,2986],{"xmlns":583,"display":584},[586,2987,2988,3048],{},[589,2989,2990,3020],{"rowspacing":591,"columnalign":592,"columnspacing":593},[595,2991,2992,3006],{},[598,2993,2994],{},[601,2995,2996],{"scriptlevel":603,"displaystyle":604},[606,2997,2998,3000,3002,3004],{},[612,2999,621],{},[623,3001,1163],{},[616,3003,668],{},[612,3005,635],{},[598,3007,3008],{},[601,3009,3010],{"scriptlevel":603,"displaystyle":604},[606,3011,3012,3014,3016,3018],{},[606,3013],{},[623,3015,646],{},[623,3017,1163],{},[616,3019,2075],{},[595,3021,3022,3036],{},[598,3023,3024],{},[601,3025,3026],{"scriptlevel":603,"displaystyle":604},[606,3027,3028,3030,3032,3034],{},[616,3029,668],{},[612,3031,621],{},[623,3033,625],{},[612,3035,635],{},[598,3037,3038],{},[601,3039,3040],{"scriptlevel":603,"displaystyle":604},[606,3041,3042,3044,3046],{},[606,3043],{},[623,3045,646],{},[616,3047,2064],{},[698,3049,3050],{"encoding":700},"\\begin{aligned} x - 2y &= -4 \\\\ 2x + y &= 7 \\end{aligned}",[568,3052,3054],{"className":3053,"ariaHidden":604},[705],[568,3055,3057,3060],{"className":3056},[709],[568,3058],{"className":3059,"style":714},[713],[568,3061,3063],{"className":3062},[718],[568,3064,3066,3141],{"className":3065},[589],[568,3067,3069],{"className":3068},[725],[568,3070,3072,3133],{"className":3071},[729,730],[568,3073,3075,3130],{"className":3074},[734],[568,3076,3078,3104],{"className":3077,"style":739},[738],[568,3079,3080,3083],{"style":742},[568,3081],{"className":3082,"style":747},[746],[568,3084,3086,3089,3092,3095,3098,3101],{"className":3085},[718],[568,3087,621],{"className":3088},[718,757],[568,3090],{"className":3091,"style":810},[809],[568,3093,1163],{"className":3094},[814],[568,3096],{"className":3097,"style":810},[809],[568,3099,668],{"className":3100},[718],[568,3102,635],{"className":3103,"style":861},[718,757],[568,3105,3106,3109],{"style":864},[568,3107],{"className":3108,"style":747},[746],[568,3110,3112,3115,3118,3121,3124,3127],{"className":3111},[718],[568,3113,668],{"className":3114},[718],[568,3116,621],{"className":3117},[718,757],[568,3119],{"className":3120,"style":810},[809],[568,3122,625],{"className":3123},[814],[568,3125],{"className":3126,"style":810},[809],[568,3128,635],{"className":3129,"style":861},[718,757],[568,3131,793],{"className":3132},[792],[568,3134,3136],{"className":3135},[734],[568,3137,3139],{"className":3138,"style":975},[738],[568,3140],{},[568,3142,3144],{"className":3143},[981],[568,3145,3147,3205],{"className":3146},[729,730],[568,3148,3150,3202],{"className":3149},[734],[568,3151,3153,3179],{"className":3152,"style":739},[738],[568,3154,3155,3158],{"style":742},[568,3156],{"className":3157,"style":747},[746],[568,3159,3161,3164,3167,3170,3173,3176],{"className":3160},[718],[568,3162],{"className":3163},[718],[568,3165],{"className":3166,"style":1005},[809],[568,3168,646],{"className":3169},[1009],[568,3171],{"className":3172,"style":1005},[809],[568,3174,1163],{"className":3175},[718],[568,3177,2075],{"className":3178},[718],[568,3180,3181,3184],{"style":864},[568,3182],{"className":3183,"style":747},[746],[568,3185,3187,3190,3193,3196,3199],{"className":3186},[718],[568,3188],{"className":3189},[718],[568,3191],{"className":3192,"style":1005},[809],[568,3194,646],{"className":3195},[1009],[568,3197],{"className":3198,"style":1005},[809],[568,3200,2064],{"className":3201},[718],[568,3203,793],{"className":3204},[792],[568,3206,3208],{"className":3207},[734],[568,3209,3211],{"className":3210,"style":975},[738],[568,3212],{},[564,3214,3215,3373],{},[568,3216,3218,3261],{"className":3217},[575],[568,3219,3221],{"className":3220},[579],[581,3222,3223],{"xmlns":583},[586,3224,3225,3258],{},[606,3226,3227,3229,3231,3233,3235,3237,3239,3241,3243,3247,3249,3251,3254,3256],{},[612,3228,1146],{},[623,3230,646],{},[616,3232,618],{},[623,3234,2288],{},[616,3236,618],{},[623,3238,1163],{},[616,3240,668],{},[623,3242,2288],{},[623,3244,3246],{"stretchy":3245},"false","(",[623,3248,1163],{},[616,3250,668],{},[623,3252,3253],{"stretchy":3245},")",[623,3255,646],{},[616,3257,2082],{},[698,3259,3260],{"encoding":700},"D = 1 \\cdot 1 - 2 \\cdot (-2) = 5",[568,3262,3264,3282,3300,3318,3336,3364],{"className":3263,"ariaHidden":604},[705],[568,3265,3267,3270,3273,3276,3279],{"className":3266},[709],[568,3268],{"className":3269,"style":1188},[713],[568,3271,1146],{"className":3272,"style":1192},[718,757],[568,3274],{"className":3275,"style":1005},[809],[568,3277,646],{"className":3278},[1009],[568,3280],{"className":3281,"style":1005},[809],[568,3283,3285,3288,3291,3294,3297],{"className":3284},[709],[568,3286],{"className":3287,"style":1486},[713],[568,3289,618],{"className":3290},[718],[568,3292],{"className":3293,"style":810},[809],[568,3295,2288],{"className":3296},[814],[568,3298],{"className":3299,"style":810},[809],[568,3301,3303,3306,3309,3312,3315],{"className":3302},[709],[568,3304],{"className":3305,"style":2351},[713],[568,3307,618],{"className":3308},[718],[568,3310],{"className":3311,"style":810},[809],[568,3313,1163],{"className":3314},[814],[568,3316],{"className":3317,"style":810},[809],[568,3319,3321,3324,3327,3330,3333],{"className":3320},[709],[568,3322],{"className":3323,"style":1486},[713],[568,3325,668],{"className":3326},[718],[568,3328],{"className":3329,"style":810},[809],[568,3331,2288],{"className":3332},[814],[568,3334],{"className":3335,"style":810},[809],[568,3337,3339,3343,3346,3349,3352,3355,3358,3361],{"className":3338},[709],[568,3340],{"className":3341,"style":3342},[713],"height:1em;vertical-align:-0.25em;",[568,3344,3246],{"className":3345},[2547],[568,3347,1163],{"className":3348},[718],[568,3350,668],{"className":3351},[718],[568,3353,3253],{"className":3354},[2648],[568,3356],{"className":3357,"style":1005},[809],[568,3359,646],{"className":3360},[1009],[568,3362],{"className":3363,"style":1005},[809],[568,3365,3367,3370],{"className":3366},[709],[568,3368],{"className":3369,"style":1486},[713],[568,3371,2082],{"className":3372},[718],", und",[568,3375,3377],{"className":3376},[571],[568,3378,3380,3488],{"className":3379},[575],[568,3381,3383],{"className":3382},[579],[581,3384,3385],{"xmlns":583,"display":584},[586,3386,3387,3485],{},[606,3388,3389,3391,3393,3425,3427,3434,3436,3438,3440,3442,3444,3446,3472,3474,3481,3483],{},[612,3390,621],{},[623,3392,646],{},[2430,3394,3395,3423],{},[606,3396,3397,3399,3401,3403,3405,3407,3409,3411,3413,3415,3417,3419,3421],{},[623,3398,3246],{"stretchy":3245},[623,3400,1163],{},[616,3402,2075],{},[623,3404,3253],{"stretchy":3245},[623,3406,2288],{},[616,3408,618],{},[623,3410,1163],{},[616,3412,2064],{},[623,3414,2288],{},[623,3416,3246],{"stretchy":3245},[623,3418,1163],{},[616,3420,668],{},[623,3422,3253],{"stretchy":3245},[616,3424,2082],{},[623,3426,646],{},[2430,3428,3429,3432],{},[616,3430,3431],{},"10",[616,3433,2082],{},[623,3435,646],{},[616,3437,668],{},[623,3439,1627],{"separator":604},[809,3441],{"width":2467},[612,3443,635],{},[623,3445,646],{},[2430,3447,3448,3470],{},[606,3449,3450,3452,3454,3456,3458,3460,3462,3464,3466,3468],{},[616,3451,618],{},[623,3453,2288],{},[616,3455,2064],{},[623,3457,1163],{},[616,3459,668],{},[623,3461,2288],{},[623,3463,3246],{"stretchy":3245},[623,3465,1163],{},[616,3467,2075],{},[623,3469,3253],{"stretchy":3245},[616,3471,2082],{},[623,3473,646],{},[2430,3475,3476,3479],{},[616,3477,3478],{},"15",[616,3480,2082],{},[623,3482,646],{},[616,3484,2043],{},[698,3486,3487],{"encoding":700},"x = \\frac{(-4) \\cdot 1 - 7 \\cdot (-2)}{5} = \\frac{10}{5} = 2, \\qquad y = \\frac{1 \\cdot 7 - 2 \\cdot (-4)}{5} = \\frac{15}{5} = 3",[568,3489,3491,3509,3642,3719,3749,3871,3948],{"className":3490,"ariaHidden":604},[705],[568,3492,3494,3497,3500,3503,3506],{"className":3493},[709],[568,3495],{"className":3496,"style":1573},[713],[568,3498,621],{"className":3499},[718,757],[568,3501],{"className":3502,"style":1005},[809],[568,3504,646],{"className":3505},[1009],[568,3507],{"className":3508,"style":1005},[809],[568,3510,3512,3516,3633,3636,3639],{"className":3511},[709],[568,3513],{"className":3514,"style":3515},[713],"height:2.113em;vertical-align:-0.686em;",[568,3517,3519,3522,3630],{"className":3518},[718],[568,3520],{"className":3521},[2547,2548],[568,3523,3525],{"className":3524},[2430],[568,3526,3528,3622],{"className":3527},[729,730],[568,3529,3531,3619],{"className":3530},[734],[568,3532,3535,3546,3554],{"className":3533,"style":3534},[738],"height:1.427em;",[568,3536,3537,3540],{"style":2564},[568,3538],{"className":3539,"style":747},[746],[568,3541,3543],{"className":3542},[718],[568,3544,2082],{"className":3545},[718],[568,3547,3548,3551],{"style":2576},[568,3549],{"className":3550,"style":747},[746],[568,3552],{"className":3553,"style":2584},[2583],[568,3555,3556,3559],{"style":2587},[568,3557],{"className":3558,"style":747},[746],[568,3560,3562,3565,3568,3571,3574,3577,3580,3583,3586,3589,3592,3595,3598,3601,3604,3607,3610,3613,3616],{"className":3561},[718],[568,3563,3246],{"className":3564},[2547],[568,3566,1163],{"className":3567},[718],[568,3569,2075],{"className":3570},[718],[568,3572,3253],{"className":3573},[2648],[568,3575],{"className":3576,"style":810},[809],[568,3578,2288],{"className":3579},[814],[568,3581],{"className":3582,"style":810},[809],[568,3584,618],{"className":3585},[718],[568,3587],{"className":3588,"style":810},[809],[568,3590,1163],{"className":3591},[814],[568,3593],{"className":3594,"style":810},[809],[568,3596,2064],{"className":3597},[718],[568,3599],{"className":3600,"style":810},[809],[568,3602,2288],{"className":3603},[814],[568,3605],{"className":3606,"style":810},[809],[568,3608,3246],{"className":3609},[2547],[568,3611,1163],{"className":3612},[718],[568,3614,668],{"className":3615},[718],[568,3617,3253],{"className":3618},[2648],[568,3620,793],{"className":3621},[792],[568,3623,3625],{"className":3624},[734],[568,3626,3628],{"className":3627,"style":2642},[738],[568,3629],{},[568,3631],{"className":3632},[2648,2548],[568,3634],{"className":3635,"style":1005},[809],[568,3637,646],{"className":3638},[1009],[568,3640],{"className":3641,"style":1005},[809],[568,3643,3645,3648,3710,3713,3716],{"className":3644},[709],[568,3646],{"className":3647,"style":2540},[713],[568,3649,3651,3654,3707],{"className":3650},[718],[568,3652],{"className":3653},[2547,2548],[568,3655,3657],{"className":3656},[2430],[568,3658,3660,3699],{"className":3659},[729,730],[568,3661,3663,3696],{"className":3662},[734],[568,3664,3666,3677,3685],{"className":3665,"style":2561},[738],[568,3667,3668,3671],{"style":2564},[568,3669],{"className":3670,"style":747},[746],[568,3672,3674],{"className":3673},[718],[568,3675,2082],{"className":3676},[718],[568,3678,3679,3682],{"style":2576},[568,3680],{"className":3681,"style":747},[746],[568,3683],{"className":3684,"style":2584},[2583],[568,3686,3687,3690],{"style":2587},[568,3688],{"className":3689,"style":747},[746],[568,3691,3693],{"className":3692},[718],[568,3694,3431],{"className":3695},[718],[568,3697,793],{"className":3698},[792],[568,3700,3702],{"className":3701},[734],[568,3703,3705],{"className":3704,"style":2642},[738],[568,3706],{},[568,3708],{"className":3709},[2648,2548],[568,3711],{"className":3712,"style":1005},[809],[568,3714,646],{"className":3715},[1009],[568,3717],{"className":3718,"style":1005},[809],[568,3720,3722,3725,3728,3731,3734,3737,3740,3743,3746],{"className":3721},[709],[568,3723],{"className":3724,"style":2741},[713],[568,3726,668],{"className":3727},[718],[568,3729,1627],{"className":3730},[1690],[568,3732],{"className":3733,"style":2751},[809],[568,3735],{"className":3736,"style":1694},[809],[568,3738,635],{"className":3739,"style":861},[718,757],[568,3741],{"className":3742,"style":1005},[809],[568,3744,646],{"className":3745},[1009],[568,3747],{"className":3748,"style":1005},[809],[568,3750,3752,3755,3862,3865,3868],{"className":3751},[709],[568,3753],{"className":3754,"style":3515},[713],[568,3756,3758,3761,3859],{"className":3757},[718],[568,3759],{"className":3760},[2547,2548],[568,3762,3764],{"className":3763},[2430],[568,3765,3767,3851],{"className":3766},[729,730],[568,3768,3770,3848],{"className":3769},[734],[568,3771,3773,3784,3792],{"className":3772,"style":3534},[738],[568,3774,3775,3778],{"style":2564},[568,3776],{"className":3777,"style":747},[746],[568,3779,3781],{"className":3780},[718],[568,3782,2082],{"className":3783},[718],[568,3785,3786,3789],{"style":2576},[568,3787],{"className":3788,"style":747},[746],[568,3790],{"className":3791,"style":2584},[2583],[568,3793,3794,3797],{"style":2587},[568,3795],{"className":3796,"style":747},[746],[568,3798,3800,3803,3806,3809,3812,3815,3818,3821,3824,3827,3830,3833,3836,3839,3842,3845],{"className":3799},[718],[568,3801,618],{"className":3802},[718],[568,3804],{"className":3805,"style":810},[809],[568,3807,2288],{"className":3808},[814],[568,3810],{"className":3811,"style":810},[809],[568,3813,2064],{"className":3814},[718],[568,3816],{"className":3817,"style":810},[809],[568,3819,1163],{"className":3820},[814],[568,3822],{"className":3823,"style":810},[809],[568,3825,668],{"className":3826},[718],[568,3828],{"className":3829,"style":810},[809],[568,3831,2288],{"className":3832},[814],[568,3834],{"className":3835,"style":810},[809],[568,3837,3246],{"className":3838},[2547],[568,3840,1163],{"className":3841},[718],[568,3843,2075],{"className":3844},[718],[568,3846,3253],{"className":3847},[2648],[568,3849,793],{"className":3850},[792],[568,3852,3854],{"className":3853},[734],[568,3855,3857],{"className":3856,"style":2642},[738],[568,3858],{},[568,3860],{"className":3861},[2648,2548],[568,3863],{"className":3864,"style":1005},[809],[568,3866,646],{"className":3867},[1009],[568,3869],{"className":3870,"style":1005},[809],[568,3872,3874,3877,3939,3942,3945],{"className":3873},[709],[568,3875],{"className":3876,"style":2540},[713],[568,3878,3880,3883,3936],{"className":3879},[718],[568,3881],{"className":3882},[2547,2548],[568,3884,3886],{"className":3885},[2430],[568,3887,3889,3928],{"className":3888},[729,730],[568,3890,3892,3925],{"className":3891},[734],[568,3893,3895,3906,3914],{"className":3894,"style":2561},[738],[568,3896,3897,3900],{"style":2564},[568,3898],{"className":3899,"style":747},[746],[568,3901,3903],{"className":3902},[718],[568,3904,2082],{"className":3905},[718],[568,3907,3908,3911],{"style":2576},[568,3909],{"className":3910,"style":747},[746],[568,3912],{"className":3913,"style":2584},[2583],[568,3915,3916,3919],{"style":2587},[568,3917],{"className":3918,"style":747},[746],[568,3920,3922],{"className":3921},[718],[568,3923,3478],{"className":3924},[718],[568,3926,793],{"className":3927},[792],[568,3929,3931],{"className":3930},[734],[568,3932,3934],{"className":3933,"style":2642},[738],[568,3935],{},[568,3937],{"className":3938},[2648,2548],[568,3940],{"className":3941,"style":1005},[809],[568,3943,646],{"className":3944},[1009],[568,3946],{"className":3947,"style":1005},[809],[568,3949,3951,3954],{"className":3950},[709],[568,3952],{"className":3953,"style":1486},[713],[568,3955,2043],{"className":3956},[718],[564,3958,3959,3960,4060,4061,4156],{},"Probe: ",[568,3961,3963,3991],{"className":3962},[575],[568,3964,3966],{"className":3965},[579],[581,3967,3968],{"xmlns":583},[586,3969,3970,3988],{},[606,3971,3972,3974,3976,3978,3980,3982,3984,3986],{},[616,3973,668],{},[623,3975,1163],{},[616,3977,668],{},[623,3979,2288],{},[616,3981,2043],{},[623,3983,646],{},[623,3985,1163],{},[616,3987,2075],{},[698,3989,3990],{"encoding":700},"2 - 2 \\cdot 3 = -4",[568,3992,3994,4012,4030,4048],{"className":3993,"ariaHidden":604},[705],[568,3995,3997,4000,4003,4006,4009],{"className":3996},[709],[568,3998],{"className":3999,"style":2351},[713],[568,4001,668],{"className":4002},[718],[568,4004],{"className":4005,"style":810},[809],[568,4007,1163],{"className":4008},[814],[568,4010],{"className":4011,"style":810},[809],[568,4013,4015,4018,4021,4024,4027],{"className":4014},[709],[568,4016],{"className":4017,"style":1486},[713],[568,4019,668],{"className":4020},[718],[568,4022],{"className":4023,"style":810},[809],[568,4025,2288],{"className":4026},[814],[568,4028],{"className":4029,"style":810},[809],[568,4031,4033,4036,4039,4042,4045],{"className":4032},[709],[568,4034],{"className":4035,"style":1486},[713],[568,4037,2043],{"className":4038},[718],[568,4040],{"className":4041,"style":1005},[809],[568,4043,646],{"className":4044},[1009],[568,4046],{"className":4047,"style":1005},[809],[568,4049,4051,4054,4057],{"className":4050},[709],[568,4052],{"className":4053,"style":2351},[713],[568,4055,1163],{"className":4056},[718],[568,4058,2075],{"className":4059},[718]," und ",[568,4062,4064,4090],{"className":4063},[575],[568,4065,4067],{"className":4066},[579],[581,4068,4069],{"xmlns":583},[586,4070,4071,4087],{},[606,4072,4073,4075,4077,4079,4081,4083,4085],{},[616,4074,668],{},[623,4076,2288],{},[616,4078,668],{},[623,4080,625],{},[616,4082,2043],{},[623,4084,646],{},[616,4086,2064],{},[698,4088,4089],{"encoding":700},"2 \\cdot 2 + 3 = 7",[568,4091,4093,4111,4129,4147],{"className":4092,"ariaHidden":604},[705],[568,4094,4096,4099,4102,4105,4108],{"className":4095},[709],[568,4097],{"className":4098,"style":1486},[713],[568,4100,668],{"className":4101},[718],[568,4103],{"className":4104,"style":810},[809],[568,4106,2288],{"className":4107},[814],[568,4109],{"className":4110,"style":810},[809],[568,4112,4114,4117,4120,4123,4126],{"className":4113},[709],[568,4115],{"className":4116,"style":2351},[713],[568,4118,668],{"className":4119},[718],[568,4121],{"className":4122,"style":810},[809],[568,4124,625],{"className":4125},[814],[568,4127],{"className":4128,"style":810},[809],[568,4130,4132,4135,4138,4141,4144],{"className":4131},[709],[568,4133],{"className":4134,"style":1486},[713],[568,4136,2043],{"className":4137},[718],[568,4139],{"className":4140,"style":1005},[809],[568,4142,646],{"className":4143},[1009],[568,4145],{"className":4146,"style":1005},[809],[568,4148,4150,4153],{"className":4149},[709],[568,4151],{"className":4152,"style":1486},[713],[568,4154,2064],{"className":4155},[718],".",[564,4158,4159,4160,4060,4244,4323,4324,4463,4464,4492,4493,4571,4572,4156],{},"Ein System ohne Lösung: Bei ",[568,4161,4163,4190],{"className":4162},[575],[568,4164,4166],{"className":4165},[579],[581,4167,4168],{"xmlns":583},[586,4169,4170,4187],{},[606,4171,4172,4174,4176,4178,4180,4182,4184],{},[616,4173,668],{},[612,4175,621],{},[623,4177,625],{},[616,4179,2075],{},[612,4181,635],{},[623,4183,646],{},[616,4185,4186],{},"6",[698,4188,4189],{"encoding":700},"2x + 4y = 6",[568,4191,4193,4214,4235],{"className":4192,"ariaHidden":604},[705],[568,4194,4196,4199,4202,4205,4208,4211],{"className":4195},[709],[568,4197],{"className":4198,"style":2351},[713],[568,4200,668],{"className":4201},[718],[568,4203,621],{"className":4204},[718,757],[568,4206],{"className":4207,"style":810},[809],[568,4209,625],{"className":4210},[814],[568,4212],{"className":4213,"style":810},[809],[568,4215,4217,4220,4223,4226,4229,4232],{"className":4216},[709],[568,4218],{"className":4219,"style":2741},[713],[568,4221,2075],{"className":4222},[718],[568,4224,635],{"className":4225,"style":861},[718,757],[568,4227],{"className":4228,"style":1005},[809],[568,4230,646],{"className":4231},[1009],[568,4233],{"className":4234,"style":1005},[809],[568,4236,4238,4241],{"className":4237},[709],[568,4239],{"className":4240,"style":1486},[713],[568,4242,4186],{"className":4243},[718],[568,4245,4247,4271],{"className":4246},[575],[568,4248,4250],{"className":4249},[579],[581,4251,4252],{"xmlns":583},[586,4253,4254,4268],{},[606,4255,4256,4258,4260,4262,4264,4266],{},[612,4257,621],{},[623,4259,625],{},[616,4261,668],{},[612,4263,635],{},[623,4265,646],{},[616,4267,2082],{},[698,4269,4270],{"encoding":700},"x + 2y = 5",[568,4272,4274,4293,4314],{"className":4273,"ariaHidden":604},[705],[568,4275,4277,4281,4284,4287,4290],{"className":4276},[709],[568,4278],{"className":4279,"style":4280},[713],"height:0.6667em;vertical-align:-0.0833em;",[568,4282,621],{"className":4283},[718,757],[568,4285],{"className":4286,"style":810},[809],[568,4288,625],{"className":4289},[814],[568,4291],{"className":4292,"style":810},[809],[568,4294,4296,4299,4302,4305,4308,4311],{"className":4295},[709],[568,4297],{"className":4298,"style":2741},[713],[568,4300,668],{"className":4301},[718],[568,4303,635],{"className":4304,"style":861},[718,757],[568,4306],{"className":4307,"style":1005},[809],[568,4309,646],{"className":4310},[1009],[568,4312],{"className":4313,"style":1005},[809],[568,4315,4317,4320],{"className":4316},[709],[568,4318],{"className":4319,"style":1486},[713],[568,4321,2082],{"className":4322},[718]," ist ",[568,4325,4327,4361],{"className":4326},[575],[568,4328,4330],{"className":4329},[579],[581,4331,4332],{"xmlns":583},[586,4333,4334,4358],{},[606,4335,4336,4338,4340,4342,4344,4346,4348,4350,4352,4354,4356],{},[612,4337,1146],{},[623,4339,646],{},[616,4341,668],{},[623,4343,2288],{},[616,4345,668],{},[623,4347,1163],{},[616,4349,618],{},[623,4351,2288],{},[616,4353,2075],{},[623,4355,646],{},[616,4357,603],{},[698,4359,4360],{"encoding":700},"D = 2 \\cdot 2 - 1 \\cdot 4 = 0",[568,4362,4364,4382,4400,4418,4436,4454],{"className":4363,"ariaHidden":604},[705],[568,4365,4367,4370,4373,4376,4379],{"className":4366},[709],[568,4368],{"className":4369,"style":1188},[713],[568,4371,1146],{"className":4372,"style":1192},[718,757],[568,4374],{"className":4375,"style":1005},[809],[568,4377,646],{"className":4378},[1009],[568,4380],{"className":4381,"style":1005},[809],[568,4383,4385,4388,4391,4394,4397],{"className":4384},[709],[568,4386],{"className":4387,"style":1486},[713],[568,4389,668],{"className":4390},[718],[568,4392],{"className":4393,"style":810},[809],[568,4395,2288],{"className":4396},[814],[568,4398],{"className":4399,"style":810},[809],[568,4401,4403,4406,4409,4412,4415],{"className":4402},[709],[568,4404],{"className":4405,"style":2351},[713],[568,4407,668],{"className":4408},[718],[568,4410],{"className":4411,"style":810},[809],[568,4413,1163],{"className":4414},[814],[568,4416],{"className":4417,"style":810},[809],[568,4419,4421,4424,4427,4430,4433],{"className":4420},[709],[568,4422],{"className":4423,"style":1486},[713],[568,4425,618],{"className":4426},[718],[568,4428],{"className":4429,"style":810},[809],[568,4431,2288],{"className":4432},[814],[568,4434],{"className":4435,"style":810},[809],[568,4437,4439,4442,4445,4448,4451],{"className":4438},[709],[568,4440],{"className":4441,"style":1486},[713],[568,4443,2075],{"className":4444},[718],[568,4446],{"className":4447,"style":1005},[809],[568,4449,646],{"className":4450},[1009],[568,4452],{"className":4453,"style":1005},[809],[568,4455,4457,4460],{"className":4456},[709],[568,4458],{"className":4459,"style":1486},[713],[568,4461,603],{"className":4462},[718],". Die erste Gleichung geteilt durch ",[568,4465,4467,4480],{"className":4466},[575],[568,4468,4470],{"className":4469},[579],[581,4471,4472],{"xmlns":583},[586,4473,4474,4478],{},[606,4475,4476],{},[616,4477,668],{},[698,4479,668],{"encoding":700},[568,4481,4483],{"className":4482,"ariaHidden":604},[705],[568,4484,4486,4489],{"className":4485},[709],[568,4487],{"className":4488,"style":1486},[713],[568,4490,668],{"className":4491},[718]," ergibt ",[568,4494,4496,4520],{"className":4495},[575],[568,4497,4499],{"className":4498},[579],[581,4500,4501],{"xmlns":583},[586,4502,4503,4517],{},[606,4504,4505,4507,4509,4511,4513,4515],{},[612,4506,621],{},[623,4508,625],{},[616,4510,668],{},[612,4512,635],{},[623,4514,646],{},[616,4516,2043],{},[698,4518,4519],{"encoding":700},"x + 2y = 3",[568,4521,4523,4541,4562],{"className":4522,"ariaHidden":604},[705],[568,4524,4526,4529,4532,4535,4538],{"className":4525},[709],[568,4527],{"className":4528,"style":4280},[713],[568,4530,621],{"className":4531},[718,757],[568,4533],{"className":4534,"style":810},[809],[568,4536,625],{"className":4537},[814],[568,4539],{"className":4540,"style":810},[809],[568,4542,4544,4547,4550,4553,4556,4559],{"className":4543},[709],[568,4545],{"className":4546,"style":2741},[713],[568,4548,668],{"className":4549},[718],[568,4551,635],{"className":4552,"style":861},[718,757],[568,4554],{"className":4555,"style":1005},[809],[568,4557,646],{"className":4558},[1009],[568,4560],{"className":4561,"style":1005},[809],[568,4563,4565,4568],{"className":4564},[709],[568,4566],{"className":4567,"style":1486},[713],[568,4569,2043],{"className":4570},[718],", das widerspricht ",[568,4573,4575,4598],{"className":4574},[575],[568,4576,4578],{"className":4577},[579],[581,4579,4580],{"xmlns":583},[586,4581,4582,4596],{},[606,4583,4584,4586,4588,4590,4592,4594],{},[612,4585,621],{},[623,4587,625],{},[616,4589,668],{},[612,4591,635],{},[623,4593,646],{},[616,4595,2082],{},[698,4597,4270],{"encoding":700},[568,4599,4601,4619,4640],{"className":4600,"ariaHidden":604},[705],[568,4602,4604,4607,4610,4613,4616],{"className":4603},[709],[568,4605],{"className":4606,"style":4280},[713],[568,4608,621],{"className":4609},[718,757],[568,4611],{"className":4612,"style":810},[809],[568,4614,625],{"className":4615},[814],[568,4617],{"className":4618,"style":810},[809],[568,4620,4622,4625,4628,4631,4634,4637],{"className":4621},[709],[568,4623],{"className":4624,"style":2741},[713],[568,4626,668],{"className":4627},[718],[568,4629,635],{"className":4630,"style":861},[718,757],[568,4632],{"className":4633,"style":1005},[809],[568,4635,646],{"className":4636},[1009],[568,4638],{"className":4639,"style":1005},[809],[568,4641,4643,4646],{"className":4642},[709],[568,4644],{"className":4645,"style":1486},[713],[568,4647,2082],{"className":4648},[718],[559,4650,4652],{"id":4651},"typische-fehler","Typische Fehler",[1390,4654,4655,4658,4712],{},[1393,4656,4657],{},"Die Zähler vertauschen oder die Reihenfolge der Produkte drehen. Ein Vorzeichenfehler im Zähler ändert das Ergebnis; immer mit einer Probe prüfen.",[1393,4659,4660,4661,4711],{},"Die Formel bei ",[568,4662,4664,4681],{"className":4663},[575],[568,4665,4667],{"className":4666},[579],[581,4668,4669],{"xmlns":583},[586,4670,4671,4679],{},[606,4672,4673,4675,4677],{},[612,4674,1146],{},[623,4676,646],{},[616,4678,603],{},[698,4680,1513],{"encoding":700},[568,4682,4684,4702],{"className":4683,"ariaHidden":604},[705],[568,4685,4687,4690,4693,4696,4699],{"className":4686},[709],[568,4688],{"className":4689,"style":1188},[713],[568,4691,1146],{"className":4692,"style":1192},[718,757],[568,4694],{"className":4695,"style":1005},[809],[568,4697,646],{"className":4698},[1009],[568,4700],{"className":4701,"style":1005},[809],[568,4703,4705,4708],{"className":4704},[709],[568,4706],{"className":4707,"style":1486},[713],[568,4709,603],{"className":4710},[718]," verwenden. Durch null darf nicht geteilt werden; das System hat dann keine eindeutige Lösung.",[1393,4713,4714,4715,4060,4743,4771],{},"Das System vorher nicht ordnen: Die Formel gilt nur, wenn ",[568,4716,4718,4731],{"className":4717},[575],[568,4719,4721],{"className":4720},[579],[581,4722,4723],{"xmlns":583},[586,4724,4725,4729],{},[606,4726,4727],{},[612,4728,621],{},[698,4730,621],{"encoding":700},[568,4732,4734],{"className":4733,"ariaHidden":604},[705],[568,4735,4737,4740],{"className":4736},[709],[568,4738],{"className":4739,"style":1573},[713],[568,4741,621],{"className":4742},[718,757],[568,4744,4746,4759],{"className":4745},[575],[568,4747,4749],{"className":4748},[579],[581,4750,4751],{"xmlns":583},[586,4752,4753,4757],{},[606,4754,4755],{},[612,4756,635],{},[698,4758,635],{"encoding":700},[568,4760,4762],{"className":4761,"ariaHidden":604},[705],[568,4763,4765,4768],{"className":4764},[709],[568,4766],{"className":4767,"style":1646},[713],[568,4769,635],{"className":4770,"style":861},[718,757]," links und die Zahlen rechts stehen.",{"title":4773,"searchDepth":4774,"depth":4774,"links":4775},"",2,[4776,4777,4778],{"id":561,"depth":4774,"text":562},{"id":2016,"depth":4774,"text":2017},{"id":4651,"depth":4774,"text":4652},[4780,4787,4791,4796,4798,4800,4802,4805,4807,4809,4811,4813,4816,4818],{"lhs":4781,"rhs":4782,"where":4783},"a1*(c1*b2 - c2*b1)\u002F(a1*b2 - a2*b1) + b1*(a1*c2 - a2*c1)\u002F(a1*b2 - a2*b1)","c1",{"a1":4784,"b1":4774,"a2":4785,"b2":4786},3,4,5,{"lhs":4788,"rhs":4789,"where":4790},"a2*(c1*b2 - c2*b1)\u002F(a1*b2 - a2*b1) + b2*(a1*c2 - a2*c1)\u002F(a1*b2 - a2*b1)","c2",{"a1":4784,"b1":4774,"a2":4785,"b2":4786},{"lhs":4781,"rhs":4782,"where":4792},{"a1":4793,"b1":4794,"a2":4795,"b2":4784},1,-2,0.5,{"lhs":4788,"rhs":4789,"where":4797},{"a1":4793,"b1":4794,"a2":4795,"b2":4784},{"lhs":4799,"rhs":2064},"3*5 - 4*2",{"lhs":4801,"rhs":2043},"(7*5 - 7*2)\u002F7",{"lhs":4803,"rhs":4804},"(3*7 - 4*7)\u002F7","-1",{"lhs":4806,"rhs":2064},"det([[3, 2], [4, 5]])",{"lhs":4808,"rhs":2082},"1*1 - 2*(-2)",{"lhs":4810,"rhs":668},"((-4)*1 - 7*(-2))\u002F5",{"lhs":4812,"rhs":2043},"(1*7 - 2*(-4))\u002F5",{"lhs":4814,"rhs":4815},"2 - 2*3","-4",{"lhs":4817,"rhs":2064},"2*2 + 3",{"lhs":4819,"rhs":603},"2*2 - 1*4","a_1 x + b_1 y = c_1,\\ a_2 x + b_2 y = c_2,\\ a_1 b_2 - a_2 b_1 \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_1 x + b_1 y = c_1,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_2 x + b_2 y = c_2,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_1 b_2 - a_2 b_1 \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","linear-system-2x2","x = \\frac{c_1 b_2 - c_2 b_1}{a_1 b_2 - a_2 b_1}, \\qquad y = \\frac{a_1 c_2 - a_2 c_1}{a_1 b_2 - a_2 b_1}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsub>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>y\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x = \\frac{c_1 b_2 - c_2 b_1}{a_1 b_2 - a_2 b_1}, \\qquad y = \\frac{a_1 c_2 - a_2 c_1}{a_1 b_2 - a_2 b_1}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.2074em;vertical-align:-0.836em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan 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