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\\end{aligned}",[573,1064,1066],{"className":1065,"ariaHidden":603},[602],[573,1067,1069,1073],{"className":1068},[607],[573,1070],{"className":1071,"style":1072},[611],"height:2.7em;vertical-align:-1.1em;",[573,1074,1076],{"className":1075},[616],[573,1077,1079,1185],{"className":1078},[984],[573,1080,1083],{"className":1081},[1082],"col-align-r",[573,1084,1088,1176],{"className":1085},[1086,1087],"vlist-t","vlist-t2",[573,1089,1092,1171],{"className":1090},[1091],"vlist-r",[573,1093,1097,1126],{"className":1094,"style":1096},[1095],"vlist","height:1.6em;",[573,1098,1100,1105],{"style":1099},"top:-3.76em;",[573,1101],{"className":1102,"style":1104},[1103],"pstrut","height:3em;",[573,1106,1108,1116,1120,1123],{"className":1107},[616],[573,1109,1112],{"className":1110},[616,1111],"text",[573,1113,1115],{"className":1114},[616],"I:",[573,1117,1119],{"className":1118},[887]," ",[573,1121,1119],{"className":1122},[887],[573,1124,633],{"className":1125,"style":649},[616,617],[573,1127,1129,1132],{"style":1128},"top:-2.26em;",[573,1130],{"className":1131,"style":1104},[1103],[573,1133,1135,1142,1145,1148,1151,1154,1158,1162,1165,1168],{"className":1134},[616],[573,1136,1138],{"className":1137},[616,1111],[573,1139,1141],{"className":1140},[616],"II:",[573,1143,1119],{"className":1144},[887],[573,1146,1119],{"className":1147},[887],[573,1149,864],{"className":1150},[616],[573,1152,594],{"className":1153},[616,617],[573,1155],{"className":1156,"style":1157},[887],"margin-right:0.2222em;",[573,1159,1042],{"className":1160},[1161],"mbin",[573,1163],{"className":1164,"style":1157},[887],[573,1166,858],{"className":1167},[616],[573,1169,633],{"className":1170,"style":649},[616,617],[573,1172,1175],{"className":1173},[1174],"vlist-s","​",[573,1177,1179],{"className":1178},[1091],[573,1180,1183],{"className":1181,"style":1182},[1095],"height:1.1em;",[573,1184],{},[573,1186,1189],{"className":1187},[1188],"col-align-l",[573,1190,1192,1262],{"className":1191},[1086,1087],[573,1193,1195,1259],{"className":1194},[1091],[573,1196,1198,1236],{"className":1197,"style":1096},[1095],[573,1199,1200,1203],{"style":1099},[573,1201],{"className":1202,"style":1104},[1103],[573,1204,1206,1209,1212,1215,1218,1221,1224,1227,1230,1233],{"className":1205},[616],[573,1207],{"className":1208},[616],[573,1210],{"className":1211,"style":888},[887],[573,1213,861],{"className":1214},[892],[573,1216],{"className":1217,"style":888},[887],[573,1219,858],{"className":1220},[616],[573,1222,594],{"className":1223},[616,617],[573,1225],{"className":1226,"style":1157},[887],[573,1228,854],{"className":1229},[1161],[573,1231],{"className":1232,"style":1157},[887],[573,1234,1024],{"className":1235},[616],[573,1237,1238,1241],{"style":1128},[573,1239],{"className":1240,"style":1104},[1103],[573,1242,1244,1247,1250,1253,1256],{"className":1243},[616],[573,1245],{"className":1246},[616],[573,1248],{"className":1249,"style":888},[887],[573,1251,861],{"className":1252},[892],[573,1254],{"className":1255,"style":888},[887],[573,1257,1059],{"className":1258},[616],[573,1260,1175],{"className":1261},[1174],[573,1263,1265],{"className":1264},[1091],[573,1266,1268],{"className":1267,"style":1182},[1095],[573,1269],{},[564,1271,1272,1273,1301],{},"I ist schon nach ",[573,1274,1276,1289],{"className":1275},[576],[573,1277,1279],{"className":1278},[580],[582,1280,1281],{"xmlns":584},[586,1282,1283,1287],{},[589,1284,1285],{},[592,1286,633],{},[596,1288,633],{"encoding":598},[573,1290,1292],{"className":1291,"ariaHidden":603},[602],[573,1293,1295,1298],{"className":1294},[607],[573,1296],{"className":1297,"style":645},[611],[573,1299,633],{"className":1300,"style":649},[616,617]," aufgelöst. Einsetzen in II:",[573,1303,1305],{"className":1304},[971],[573,1306,1308,1380],{"className":1307},[576],[573,1309,1311],{"className":1310},[580],[582,1312,1313],{"xmlns":584,"display":980},[586,1314,1315,1377],{},[589,1316,1317,1319,1321,1323,1325,1329,1331,1333,1335,1337,1340,1342,1344,1347,1350,1352,1355,1357,1359,1361,1363,1365,1367,1369,1371,1373,1375],{},[856,1318,864],{},[592,1320,594],{},[852,1322,1042],{},[856,1324,858],{},[852,1326,1328],{"stretchy":1327},"false","(",[856,1330,858],{},[592,1332,594],{},[852,1334,854],{},[856,1336,1024],{},[852,1338,1339],{"stretchy":1327},")",[852,1341,861],{},[856,1343,1059],{},[1001,1345,1346],{},"  ",[852,1348,1349],{},"⇒",[1001,1351,1346],{},[856,1353,1354],{},"7",[592,1356,594],{},[852,1358,854],{},[856,1360,858],{},[852,1362,861],{},[856,1364,1059],{},[1001,1366,1346],{},[852,1368,1349],{},[1001,1370,1346],{},[592,1372,594],{},[852,1374,861],{},[856,1376,858],{},[596,1378,1379],{"encoding":598},"3x + 2(2x - 1) = 12 \\;\\Rightarrow\\; 7x - 2 = 12 \\;\\Rightarrow\\; x = 2",[573,1381,1383,1404,1433,1455,1479,1500,1518,1542,1560],{"className":1382,"ariaHidden":603},[602],[573,1384,1386,1389,1392,1395,1398,1401],{"className":1385},[607],[573,1387],{"className":1388,"style":877},[611],[573,1390,864],{"className":1391},[616],[573,1393,594],{"className":1394},[616,617],[573,1396],{"className":1397,"style":1157},[887],[573,1399,1042],{"className":1400},[1161],[573,1402],{"className":1403,"style":1157},[887],[573,1405,1407,1411,1414,1418,1421,1424,1427,1430],{"className":1406},[607],[573,1408],{"className":1409,"style":1410},[611],"height:1em;vertical-align:-0.25em;",[573,1412,858],{"className":1413},[616],[573,1415,1328],{"className":1416},[1417],"mopen",[573,1419,858],{"className":1420},[616],[573,1422,594],{"className":1423},[616,617],[573,1425],{"className":1426,"style":1157},[887],[573,1428,854],{"className":1429},[1161],[573,1431],{"className":1432,"style":1157},[887],[573,1434,1436,1439,1442,1446,1449,1452],{"className":1435},[607],[573,1437],{"className":1438,"style":1410},[611],[573,1440,1024],{"className":1441},[616],[573,1443,1339],{"className":1444},[1445],"mclose",[573,1447],{"className":1448,"style":888},[887],[573,1450,861],{"className":1451},[892],[573,1453],{"className":1454,"style":888},[887],[573,1456,1458,1461,1464,1467,1470,1473,1476],{"className":1457},[607],[573,1459],{"className":1460,"style":902},[611],[573,1462,1059],{"className":1463},[616],[573,1465],{"className":1466,"style":888},[887],[573,1468],{"className":1469,"style":888},[887],[573,1471,1349],{"className":1472},[892],[573,1474],{"className":1475,"style":888},[887],[573,1477],{"className":1478,"style":888},[887],[573,1480,1482,1485,1488,1491,1494,1497],{"className":1481},[607],[573,1483],{"className":1484,"style":877},[611],[573,1486,1354],{"className":1487},[616],[573,1489,594],{"className":1490},[616,617],[573,1492],{"className":1493,"style":1157},[887],[573,1495,854],{"className":1496},[1161],[573,1498],{"className":1499,"style":1157},[887],[573,1501,1503,1506,1509,1512,1515],{"className":1502},[607],[573,1504],{"className":1505,"style":902},[611],[573,1507,858],{"className":1508},[616],[573,1510],{"className":1511,"style":888},[887],[573,1513,861],{"className":1514},[892],[573,1516],{"className":1517,"style":888},[887],[573,1519,1521,1524,1527,1530,1533,1536,1539],{"className":1520},[607],[573,1522],{"className":1523,"style":902},[611],[573,1525,1059],{"className":1526},[616],[573,1528],{"className":1529,"style":888},[887],[573,1531],{"className":1532,"style":888},[887],[573,1534,1349],{"className":1535},[892],[573,1537],{"className":1538,"style":888},[887],[573,1540],{"className":1541,"style":888},[887],[573,1543,1545,1548,1551,1554,1557],{"className":1544},[607],[573,1546],{"className":1547,"style":612},[611],[573,1549,594],{"className":1550},[616,617],[573,1552],{"className":1553,"style":888},[887],[573,1555,861],{"className":1556},[892],[573,1558],{"className":1559,"style":888},[887],[573,1561,1563,1566],{"className":1562},[607],[573,1564],{"className":1565,"style":902},[611],[573,1567,858],{"className":1568},[616],[564,1570,1571,1572,1690,1691,1808,1809,1871],{},"Dann ",[573,1573,1575,1606],{"className":1574},[576],[573,1576,1578],{"className":1577},[580],[582,1579,1580],{"xmlns":584},[586,1581,1582,1603],{},[589,1583,1584,1586,1588,1590,1593,1595,1597,1599,1601],{},[592,1585,633],{},[852,1587,861],{},[856,1589,858],{},[852,1591,1592],{},"⋅",[856,1594,858],{},[852,1596,854],{},[856,1598,1024],{},[852,1600,861],{},[856,1602,864],{},[596,1604,1605],{"encoding":598},"y = 2 \\cdot 2 - 1 = 3",[573,1607,1609,1627,1645,1663,1681],{"className":1608,"ariaHidden":603},[602],[573,1610,1612,1615,1618,1621,1624],{"className":1611},[607],[573,1613],{"className":1614,"style":645},[611],[573,1616,633],{"className":1617,"style":649},[616,617],[573,1619],{"className":1620,"style":888},[887],[573,1622,861],{"className":1623},[892],[573,1625],{"className":1626,"style":888},[887],[573,1628,1630,1633,1636,1639,1642],{"className":1629},[607],[573,1631],{"className":1632,"style":902},[611],[573,1634,858],{"className":1635},[616],[573,1637],{"className":1638,"style":1157},[887],[573,1640,1592],{"className":1641},[1161],[573,1643],{"className":1644,"style":1157},[887],[573,1646,1648,1651,1654,1657,1660],{"className":1647},[607],[573,1649],{"className":1650,"style":877},[611],[573,1652,858],{"className":1653},[616],[573,1655],{"className":1656,"style":1157},[887],[573,1658,854],{"className":1659},[1161],[573,1661],{"className":1662,"style":1157},[887],[573,1664,1666,1669,1672,1675,1678],{"className":1665},[607],[573,1667],{"className":1668,"style":902},[611],[573,1670,1024],{"className":1671},[616],[573,1673],{"className":1674,"style":888},[887],[573,1676,861],{"className":1677},[892],[573,1679],{"className":1680,"style":888},[887],[573,1682,1684,1687],{"className":1683},[607],[573,1685],{"className":1686,"style":902},[611],[573,1688,864],{"className":1689},[616],". Probe in II: ",[573,1692,1694,1724],{"className":1693},[576],[573,1695,1697],{"className":1696},[580],[582,1698,1699],{"xmlns":584},[586,1700,1701,1721],{},[589,1702,1703,1705,1707,1709,1711,1713,1715,1717,1719],{},[856,1704,864],{},[852,1706,1592],{},[856,1708,858],{},[852,1710,1042],{},[856,1712,858],{},[852,1714,1592],{},[856,1716,864],{},[852,1718,861],{},[856,1720,1059],{},[596,1722,1723],{"encoding":598},"3 \\cdot 2 + 2 \\cdot 3 = 12",[573,1725,1727,1745,1763,1781,1799],{"className":1726,"ariaHidden":603},[602],[573,1728,1730,1733,1736,1739,1742],{"className":1729},[607],[573,1731],{"className":1732,"style":902},[611],[573,1734,864],{"className":1735},[616],[573,1737],{"className":1738,"style":1157},[887],[573,1740,1592],{"className":1741},[1161],[573,1743],{"className":1744,"style":1157},[887],[573,1746,1748,1751,1754,1757,1760],{"className":1747},[607],[573,1749],{"className":1750,"style":877},[611],[573,1752,858],{"className":1753},[616],[573,1755],{"className":1756,"style":1157},[887],[573,1758,1042],{"className":1759},[1161],[573,1761],{"className":1762,"style":1157},[887],[573,1764,1766,1769,1772,1775,1778],{"className":1765},[607],[573,1767],{"className":1768,"style":902},[611],[573,1770,858],{"className":1771},[616],[573,1773],{"className":1774,"style":1157},[887],[573,1776,1592],{"className":1777},[1161],[573,1779],{"className":1780,"style":1157},[887],[573,1782,1784,1787,1790,1793,1796],{"className":1783},[607],[573,1785],{"className":1786,"style":902},[611],[573,1788,864],{"className":1789},[616],[573,1791],{"className":1792,"style":888},[887],[573,1794,861],{"className":1795},[892],[573,1797],{"className":1798,"style":888},[887],[573,1800,1802,1805],{"className":1801},[607],[573,1803],{"className":1804,"style":902},[611],[573,1806,1059],{"className":1807},[616],". Die Lösung ist ",[573,1810,1812,1835],{"className":1811},[576],[573,1813,1815],{"className":1814},[580],[582,1816,1817],{"xmlns":584},[586,1818,1819,1832],{},[589,1820,1821,1823,1825,1828,1830],{},[852,1822,1328],{"stretchy":1327},[856,1824,858],{},[852,1826,1827],{},"∣",[856,1829,864],{},[852,1831,1339],{"stretchy":1327},[596,1833,1834],{"encoding":598},"(2 \\mid 3)",[573,1836,1838,1859],{"className":1837,"ariaHidden":603},[602],[573,1839,1841,1844,1847,1850,1853,1856],{"className":1840},[607],[573,1842],{"className":1843,"style":1410},[611],[573,1845,1328],{"className":1846},[1417],[573,1848,858],{"className":1849},[616],[573,1851],{"className":1852,"style":888},[887],[573,1854,1827],{"className":1855},[892],[573,1857],{"className":1858,"style":888},[887],[573,1860,1862,1865,1868],{"className":1861},[607],[573,1863],{"className":1864,"style":1410},[611],[573,1866,864],{"className":1867},[616],[573,1869,1339],{"className":1870},[1445],".",[564,1873,1874],{},"Zweites Beispiel, hier wird zuerst aufgelöst:",[573,1876,1878],{"className":1877},[971],[573,1879,1881,1953],{"className":1880},[576],[573,1882,1884],{"className":1883},[580],[582,1885,1886],{"xmlns":584,"display":980},[586,1887,1888,1950],{},[984,1889,1890,1920],{"rowspacing":986,"columnalign":987,"columnspacing":988},[990,1891,1892,1908],{},[993,1893,1894],{},[996,1895,1896],{"scriptlevel":925,"displaystyle":603},[589,1897,1898,1900,1902,1904,1906],{},[1001,1899,1003],{},[592,1901,594],{},[852,1903,1042],{},[856,1905,864],{},[592,1907,633],{},[993,1909,1910],{},[996,1911,1912],{"scriptlevel":925,"displaystyle":603},[589,1913,1914,1916,1918],{},[589,1915],{},[852,1917,861],{},[856,1919,1354],{},[990,1921,1922,1938],{},[993,1923,1924],{},[996,1925,1926],{"scriptlevel":925,"displaystyle":603},[589,1927,1928,1930,1932,1934,1936],{},[1001,1929,1035],{},[856,1931,858],{},[592,1933,594],{},[852,1935,854],{},[592,1937,633],{},[993,1939,1940],{},[996,1941,1942],{"scriptlevel":925,"displaystyle":603},[589,1943,1944,1946,1948],{},[589,1945],{},[852,1947,861],{},[856,1949,925],{},[596,1951,1952],{"encoding":598},"\\begin{aligned} \\text{I:}\\ \\ x + 3y &= 7 \\\\ \\text{II:}\\ \\ 2x - y &= 0 \\end{aligned}",[573,1954,1956],{"className":1955,"ariaHidden":603},[602],[573,1957,1959,1962],{"className":1958},[607],[573,1960],{"className":1961,"style":1072},[611],[573,1963,1965],{"className":1964},[616],[573,1966,1968,2067],{"className":1967},[984],[573,1969,1971],{"className":1970},[1082],[573,1972,1974,2059],{"className":1973},[1086,1087],[573,1975,1977,2056],{"className":1976},[1091],[573,1978,1980,2018],{"className":1979,"style":1096},[1095],[573,1981,1982,1985],{"style":1099},[573,1983],{"className":1984,"style":1104},[1103],[573,1986,1988,1994,1997,2000,2003,2006,2009,2012,2015],{"className":1987},[616],[573,1989,1991],{"className":1990},[616,1111],[573,1992,1115],{"className":1993},[616],[573,1995,1119],{"className":1996},[887],[573,1998,1119],{"className":1999},[887],[573,2001,594],{"className":2002},[616,617],[573,2004],{"className":2005,"style":1157},[887],[573,2007,1042],{"className":2008},[1161],[573,2010],{"className":2011,"style":1157},[887],[573,2013,864],{"className":2014},[616],[573,2016,633],{"className":2017,"style":649},[616,617],[573,2019,2020,2023],{"style":1128},[573,2021],{"className":2022,"style":1104},[1103],[573,2024,2026,2032,2035,2038,2041,2044,2047,2050,2053],{"className":2025},[616],[573,2027,2029],{"className":2028},[616,1111],[573,2030,1141],{"className":2031},[616],[573,2033,1119],{"className":2034},[887],[573,2036,1119],{"className":2037},[887],[573,2039,858],{"className":2040},[616],[573,2042,594],{"className":2043},[616,617],[573,2045],{"className":2046,"style":1157},[887],[573,2048,854],{"className":2049},[1161],[573,2051],{"className":2052,"style":1157},[887],[573,2054,633],{"className":2055,"style":649},[616,617],[573,2057,1175],{"className":2058},[1174],[573,2060,2062],{"className":2061},[1091],[573,2063,2065],{"className":2064,"style":1182},[1095],[573,2066],{},[573,2068,2070],{"className":2069},[1188],[573,2071,2073,2128],{"className":2072},[1086,1087],[573,2074,2076,2125],{"className":2075},[1091],[573,2077,2079,2102],{"className":2078,"style":1096},[1095],[573,2080,2081,2084],{"style":1099},[573,2082],{"className":2083,"style":1104},[1103],[573,2085,2087,2090,2093,2096,2099],{"className":2086},[616],[573,2088],{"className":2089},[616],[573,2091],{"className":2092,"style":888},[887],[573,2094,861],{"className":2095},[892],[573,2097],{"className":2098,"style":888},[887],[573,2100,1354],{"className":2101},[616],[573,2103,2104,2107],{"style":1128},[573,2105],{"className":2106,"style":1104},[1103],[573,2108,2110,2113,2116,2119,2122],{"className":2109},[616],[573,2111],{"className":2112},[616],[573,2114],{"className":2115,"style":888},[887],[573,2117,861],{"className":2118},[892],[573,2120],{"className":2121,"style":888},[887],[573,2123,925],{"className":2124},[616],[573,2126,1175],{"className":2127},[1174],[573,2129,2131],{"className":2130},[1091],[573,2132,2134],{"className":2133,"style":1182},[1095],[573,2135],{},[564,2137,2138,2139,2218],{},"Aus I folgt ",[573,2140,2142,2166],{"className":2141},[576],[573,2143,2145],{"className":2144},[580],[582,2146,2147],{"xmlns":584},[586,2148,2149,2163],{},[589,2150,2151,2153,2155,2157,2159,2161],{},[592,2152,594],{},[852,2154,861],{},[856,2156,1354],{},[852,2158,854],{},[856,2160,864],{},[592,2162,633],{},[596,2164,2165],{"encoding":598},"x = 7 - 3y",[573,2167,2169,2187,2205],{"className":2168,"ariaHidden":603},[602],[573,2170,2172,2175,2178,2181,2184],{"className":2171},[607],[573,2173],{"className":2174,"style":612},[611],[573,2176,594],{"className":2177},[616,617],[573,2179],{"className":2180,"style":888},[887],[573,2182,861],{"className":2183},[892],[573,2185],{"className":2186,"style":888},[887],[573,2188,2190,2193,2196,2199,2202],{"className":2189},[607],[573,2191],{"className":2192,"style":877},[611],[573,2194,1354],{"className":2195},[616],[573,2197],{"className":2198,"style":1157},[887],[573,2200,854],{"className":2201},[1161],[573,2203],{"className":2204,"style":1157},[887],[573,2206,2208,2212,2215],{"className":2207},[607],[573,2209],{"className":2210,"style":2211},[611],"height:0.8389em;vertical-align:-0.1944em;",[573,2213,864],{"className":2214},[616],[573,2216,633],{"className":2217,"style":649},[616,617],". Einsetzen in II:",[573,2220,2222],{"className":2221},[971],[573,2223,2225,2290],{"className":2224},[576],[573,2226,2228],{"className":2227},[580],[582,2229,2230],{"xmlns":584,"display":980},[586,2231,2232,2287],{},[589,2233,2234,2236,2238,2240,2242,2244,2246,2248,2250,2252,2254,2256,2258,2260,2262,2265,2267,2269,2271,2273,2275,2277,2279,2281,2283,2285],{},[856,2235,858],{},[852,2237,1328],{"stretchy":1327},[856,2239,1354],{},[852,2241,854],{},[856,2243,864],{},[592,2245,633],{},[852,2247,1339],{"stretchy":1327},[852,2249,854],{},[592,2251,633],{},[852,2253,861],{},[856,2255,925],{},[1001,2257,1346],{},[852,2259,1349],{},[1001,2261,1346],{},[856,2263,2264],{},"14",[852,2266,854],{},[856,2268,1354],{},[592,2270,633],{},[852,2272,861],{},[856,2274,925],{},[1001,2276,1346],{},[852,2278,1349],{},[1001,2280,1346],{},[592,2282,633],{},[852,2284,861],{},[856,2286,858],{},[596,2288,2289],{"encoding":598},"2(7 - 3y) - y = 0 \\;\\Rightarrow\\; 14 - 7y = 0 \\;\\Rightarrow\\; y = 2",[573,2291,2293,2317,2341,2359,2383,2401,2422,2446,2464],{"className":2292,"ariaHidden":603},[602],[573,2294,2296,2299,2302,2305,2308,2311,2314],{"className":2295},[607],[573,2297],{"className":2298,"style":1410},[611],[573,2300,858],{"className":2301},[616],[573,2303,1328],{"className":2304},[1417],[573,2306,1354],{"className":2307},[616],[573,2309],{"className":2310,"style":1157},[887],[573,2312,854],{"className":2313},[1161],[573,2315],{"className":2316,"style":1157},[887],[573,2318,2320,2323,2326,2329,2332,2335,2338],{"className":2319},[607],[573,2321],{"className":2322,"style":1410},[611],[573,2324,864],{"className":2325},[616],[573,2327,633],{"className":2328,"style":649},[616,617],[573,2330,1339],{"className":2331},[1445],[573,2333],{"className":2334,"style":1157},[887],[573,2336,854],{"className":2337},[1161],[573,2339],{"className":2340,"style":1157},[887],[573,2342,2344,2347,2350,2353,2356],{"className":2343},[607],[573,2345],{"className":2346,"style":645},[611],[573,2348,633],{"className":2349,"style":649},[616,617],[573,2351],{"className":2352,"style":888},[887],[573,2354,861],{"className":2355},[892],[573,2357],{"className":2358,"style":888},[887],[573,2360,2362,2365,2368,2371,2374,2377,2380],{"className":2361},[607],[573,2363],{"className":2364,"style":902},[611],[573,2366,925],{"className":2367},[616],[573,2369],{"className":2370,"style":888},[887],[573,2372],{"className":2373,"style":888},[887],[573,2375,1349],{"className":2376},[892],[573,2378],{"className":2379,"style":888},[887],[573,2381],{"className":2382,"style":888},[887],[573,2384,2386,2389,2392,2395,2398],{"className":2385},[607],[573,2387],{"className":2388,"style":877},[611],[573,2390,2264],{"className":2391},[616],[573,2393],{"className":2394,"style":1157},[887],[573,2396,854],{"className":2397},[1161],[573,2399],{"className":2400,"style":1157},[887],[573,2402,2404,2407,2410,2413,2416,2419],{"className":2403},[607],[573,2405],{"className":2406,"style":2211},[611],[573,2408,1354],{"className":2409},[616],[573,2411,633],{"className":2412,"style":649},[616,617],[573,2414],{"className":2415,"style":888},[887],[573,2417,861],{"className":2418},[892],[573,2420],{"className":2421,"style":888},[887],[573,2423,2425,2428,2431,2434,2437,2440,2443],{"className":2424},[607],[573,2426],{"className":2427,"style":902},[611],[573,2429,925],{"className":2430},[616],[573,2432],{"className":2433,"style":888},[887],[573,2435],{"className":2436,"style":888},[887],[573,2438,1349],{"className":2439},[892],[573,2441],{"className":2442,"style":888},[887],[573,2444],{"className":2445,"style":888},[887],[573,2447,2449,2452,2455,2458,2461],{"className":2448},[607],[573,2450],{"className":2451,"style":645},[611],[573,2453,633],{"className":2454,"style":649},[616,617],[573,2456],{"className":2457,"style":888},[887],[573,2459,861],{"className":2460},[892],[573,2462],{"className":2463,"style":888},[887],[573,2465,2467,2470],{"className":2466},[607],[573,2468],{"className":2469,"style":902},[611],[573,2471,858],{"className":2472},[616],[564,2474,1571,2475,2592,2593,618,2688,1808,2783,1871],{},[573,2476,2478,2508],{"className":2477},[576],[573,2479,2481],{"className":2480},[580],[582,2482,2483],{"xmlns":584},[586,2484,2485,2505],{},[589,2486,2487,2489,2491,2493,2495,2497,2499,2501,2503],{},[592,2488,594],{},[852,2490,861],{},[856,2492,1354],{},[852,2494,854],{},[856,2496,864],{},[852,2498,1592],{},[856,2500,858],{},[852,2502,861],{},[856,2504,1024],{},[596,2506,2507],{"encoding":598},"x = 7 - 3 \\cdot 2 = 1",[573,2509,2511,2529,2547,2565,2583],{"className":2510,"ariaHidden":603},[602],[573,2512,2514,2517,2520,2523,2526],{"className":2513},[607],[573,2515],{"className":2516,"style":612},[611],[573,2518,594],{"className":2519},[616,617],[573,2521],{"className":2522,"style":888},[887],[573,2524,861],{"className":2525},[892],[573,2527],{"className":2528,"style":888},[887],[573,2530,2532,2535,2538,2541,2544],{"className":2531},[607],[573,2533],{"className":2534,"style":877},[611],[573,2536,1354],{"className":2537},[616],[573,2539],{"className":2540,"style":1157},[887],[573,2542,854],{"className":2543},[1161],[573,2545],{"className":2546,"style":1157},[887],[573,2548,2550,2553,2556,2559,2562],{"className":2549},[607],[573,2551],{"className":2552,"style":902},[611],[573,2554,864],{"className":2555},[616],[573,2557],{"className":2558,"style":1157},[887],[573,2560,1592],{"className":2561},[1161],[573,2563],{"className":2564,"style":1157},[887],[573,2566,2568,2571,2574,2577,2580],{"className":2567},[607],[573,2569],{"className":2570,"style":902},[611],[573,2572,858],{"className":2573},[616],[573,2575],{"className":2576,"style":888},[887],[573,2578,861],{"className":2579},[892],[573,2581],{"className":2582,"style":888},[887],[573,2584,2586,2589],{"className":2585},[607],[573,2587],{"className":2588,"style":902},[611],[573,2590,1024],{"className":2591},[616],". Probe: ",[573,2594,2596,2622],{"className":2595},[576],[573,2597,2599],{"className":2598},[580],[582,2600,2601],{"xmlns":584},[586,2602,2603,2619],{},[589,2604,2605,2607,2609,2611,2613,2615,2617],{},[856,2606,1024],{},[852,2608,1042],{},[856,2610,864],{},[852,2612,1592],{},[856,2614,858],{},[852,2616,861],{},[856,2618,1354],{},[596,2620,2621],{"encoding":598},"1 + 3 \\cdot 2 = 7",[573,2623,2625,2643,2661,2679],{"className":2624,"ariaHidden":603},[602],[573,2626,2628,2631,2634,2637,2640],{"className":2627},[607],[573,2629],{"className":2630,"style":877},[611],[573,2632,1024],{"className":2633},[616],[573,2635],{"className":2636,"style":1157},[887],[573,2638,1042],{"className":2639},[1161],[573,2641],{"className":2642,"style":1157},[887],[573,2644,2646,2649,2652,2655,2658],{"className":2645},[607],[573,2647],{"className":2648,"style":902},[611],[573,2650,864],{"className":2651},[616],[573,2653],{"className":2654,"style":1157},[887],[573,2656,1592],{"className":2657},[1161],[573,2659],{"className":2660,"style":1157},[887],[573,2662,2664,2667,2670,2673,2676],{"className":2663},[607],[573,2665],{"className":2666,"style":902},[611],[573,2668,858],{"className":2669},[616],[573,2671],{"className":2672,"style":888},[887],[573,2674,861],{"className":2675},[892],[573,2677],{"className":2678,"style":888},[887],[573,2680,2682,2685],{"className":2681},[607],[573,2683],{"className":2684,"style":902},[611],[573,2686,1354],{"className":2687},[616],[573,2689,2691,2717],{"className":2690},[576],[573,2692,2694],{"className":2693},[580],[582,2695,2696],{"xmlns":584},[586,2697,2698,2714],{},[589,2699,2700,2702,2704,2706,2708,2710,2712],{},[856,2701,858],{},[852,2703,1592],{},[856,2705,1024],{},[852,2707,854],{},[856,2709,858],{},[852,2711,861],{},[856,2713,925],{},[596,2715,2716],{"encoding":598},"2 \\cdot 1 - 2 = 0",[573,2718,2720,2738,2756,2774],{"className":2719,"ariaHidden":603},[602],[573,2721,2723,2726,2729,2732,2735],{"className":2722},[607],[573,2724],{"className":2725,"style":902},[611],[573,2727,858],{"className":2728},[616],[573,2730],{"className":2731,"style":1157},[887],[573,2733,1592],{"className":2734},[1161],[573,2736],{"className":2737,"style":1157},[887],[573,2739,2741,2744,2747,2750,2753],{"className":2740},[607],[573,2742],{"className":2743,"style":877},[611],[573,2745,1024],{"className":2746},[616],[573,2748],{"className":2749,"style":1157},[887],[573,2751,854],{"className":2752},[1161],[573,2754],{"className":2755,"style":1157},[887],[573,2757,2759,2762,2765,2768,2771],{"className":2758},[607],[573,2760],{"className":2761,"style":902},[611],[573,2763,858],{"className":2764},[616],[573,2766],{"className":2767,"style":888},[887],[573,2769,861],{"className":2770},[892],[573,2772],{"className":2773,"style":888},[887],[573,2775,2777,2780],{"className":2776},[607],[573,2778],{"className":2779,"style":902},[611],[573,2781,925],{"className":2782},[616],[573,2784,2786,2808],{"className":2785},[576],[573,2787,2789],{"className":2788},[580],[582,2790,2791],{"xmlns":584},[586,2792,2793,2805],{},[589,2794,2795,2797,2799,2801,2803],{},[852,2796,1328],{"stretchy":1327},[856,2798,1024],{},[852,2800,1827],{},[856,2802,858],{},[852,2804,1339],{"stretchy":1327},[596,2806,2807],{"encoding":598},"(1 \\mid 2)",[573,2809,2811,2832],{"className":2810,"ariaHidden":603},[602],[573,2812,2814,2817,2820,2823,2826,2829],{"className":2813},[607],[573,2815],{"className":2816,"style":1410},[611],[573,2818,1328],{"className":2819},[1417],[573,2821,1024],{"className":2822},[616],[573,2824],{"className":2825,"style":888},[887],[573,2827,1827],{"className":2828},[892],[573,2830],{"className":2831,"style":888},[887],[573,2833,2835,2838,2841],{"className":2834},[607],[573,2836],{"className":2837,"style":1410},[611],[573,2839,858],{"className":2840},[616],[573,2842,1339],{"className":2843},[1445],[564,2845,2846,2847,618,2925,3009,3010,3130,3131,3186,3187,3189],{},"Sonderfall: Aus ",[573,2848,2850,2874],{"className":2849},[576],[573,2851,2853],{"className":2852},[580],[582,2854,2855],{"xmlns":584},[586,2856,2857,2871],{},[589,2858,2859,2861,2863,2865,2867,2869],{},[592,2860,633],{},[852,2862,861],{},[856,2864,858],{},[592,2866,594],{},[852,2868,1042],{},[856,2870,1024],{},[596,2872,2873],{"encoding":598},"y = 2x + 1",[573,2875,2877,2895,2916],{"className":2876,"ariaHidden":603},[602],[573,2878,2880,2883,2886,2889,2892],{"className":2879},[607],[573,2881],{"className":2882,"style":645},[611],[573,2884,633],{"className":2885,"style":649},[616,617],[573,2887],{"className":2888,"style":888},[887],[573,2890,861],{"className":2891},[892],[573,2893],{"className":2894,"style":888},[887],[573,2896,2898,2901,2904,2907,2910,2913],{"className":2897},[607],[573,2899],{"className":2900,"style":877},[611],[573,2902,858],{"className":2903},[616],[573,2905,594],{"className":2906},[616,617],[573,2908],{"className":2909,"style":1157},[887],[573,2911,1042],{"className":2912},[1161],[573,2914],{"className":2915,"style":1157},[887],[573,2917,2919,2922],{"className":2918},[607],[573,2920],{"className":2921,"style":902},[611],[573,2923,1024],{"className":2924},[616],[573,2926,2928,2955],{"className":2927},[576],[573,2929,2931],{"className":2930},[580],[582,2932,2933],{"xmlns":584},[586,2934,2935,2952],{},[589,2936,2937,2940,2942,2944,2946,2948,2950],{},[856,2938,2939],{},"4",[592,2941,594],{},[852,2943,854],{},[856,2945,858],{},[592,2947,633],{},[852,2949,861],{},[856,2951,864],{},[596,2953,2954],{"encoding":598},"4x - 2y = 3",[573,2956,2958,2979,3000],{"className":2957,"ariaHidden":603},[602],[573,2959,2961,2964,2967,2970,2973,2976],{"className":2960},[607],[573,2962],{"className":2963,"style":877},[611],[573,2965,2939],{"className":2966},[616],[573,2968,594],{"className":2969},[616,617],[573,2971],{"className":2972,"style":1157},[887],[573,2974,854],{"className":2975},[1161],[573,2977],{"className":2978,"style":1157},[887],[573,2980,2982,2985,2988,2991,2994,2997],{"className":2981},[607],[573,2983],{"className":2984,"style":2211},[611],[573,2986,858],{"className":2987},[616],[573,2989,633],{"className":2990,"style":649},[616,617],[573,2992],{"className":2993,"style":888},[887],[573,2995,861],{"className":2996},[892],[573,2998],{"className":2999,"style":888},[887],[573,3001,3003,3006],{"className":3002},[607],[573,3004],{"className":3005,"style":902},[611],[573,3007,864],{"className":3008},[616]," wird ",[573,3011,3013,3049],{"className":3012},[576],[573,3014,3016],{"className":3015},[580],[582,3017,3018],{"xmlns":584},[586,3019,3020,3046],{},[589,3021,3022,3024,3026,3028,3030,3032,3034,3036,3038,3040,3042,3044],{},[856,3023,2939],{},[592,3025,594],{},[852,3027,854],{},[856,3029,858],{},[852,3031,1328],{"stretchy":1327},[856,3033,858],{},[592,3035,594],{},[852,3037,1042],{},[856,3039,1024],{},[852,3041,1339],{"stretchy":1327},[852,3043,861],{},[856,3045,864],{},[596,3047,3048],{"encoding":598},"4x - 2(2x + 1) = 3",[573,3050,3052,3073,3100,3121],{"className":3051,"ariaHidden":603},[602],[573,3053,3055,3058,3061,3064,3067,3070],{"className":3054},[607],[573,3056],{"className":3057,"style":877},[611],[573,3059,2939],{"className":3060},[616],[573,3062,594],{"className":3063},[616,617],[573,3065],{"className":3066,"style":1157},[887],[573,3068,854],{"className":3069},[1161],[573,3071],{"className":3072,"style":1157},[887],[573,3074,3076,3079,3082,3085,3088,3091,3094,3097],{"className":3075},[607],[573,3077],{"className":3078,"style":1410},[611],[573,3080,858],{"className":3081},[616],[573,3083,1328],{"className":3084},[1417],[573,3086,858],{"className":3087},[616],[573,3089,594],{"className":3090},[616,617],[573,3092],{"className":3093,"style":1157},[887],[573,3095,1042],{"className":3096},[1161],[573,3098],{"className":3099,"style":1157},[887],[573,3101,3103,3106,3109,3112,3115,3118],{"className":3102},[607],[573,3104],{"className":3105,"style":1410},[611],[573,3107,1024],{"className":3108},[616],[573,3110,1339],{"className":3111},[1445],[573,3113],{"className":3114,"style":888},[887],[573,3116,861],{"className":3117},[892],[573,3119],{"className":3120,"style":888},[887],[573,3122,3124,3127],{"className":3123},[607],[573,3125],{"className":3126,"style":902},[611],[573,3128,864],{"className":3129},[616],", also ",[573,3132,3134,3153],{"className":3133},[576],[573,3135,3137],{"className":3136},[580],[582,3138,3139],{"xmlns":584},[586,3140,3141,3151],{},[589,3142,3143,3145,3147,3149],{},[852,3144,854],{},[856,3146,858],{},[852,3148,861],{},[856,3150,864],{},[596,3152,867],{"encoding":598},[573,3154,3156,3177],{"className":3155,"ariaHidden":603},[602],[573,3157,3159,3162,3165,3168,3171,3174],{"className":3158},[607],[573,3160],{"className":3161,"style":877},[611],[573,3163,854],{"className":3164},[616],[573,3166,858],{"className":3167},[616],[573,3169],{"className":3170,"style":888},[887],[573,3172,861],{"className":3173},[892],[573,3175],{"className":3176,"style":888},[887],[573,3178,3180,3183],{"className":3179},[607],[573,3181],{"className":3182,"style":902},[611],[573,3184,864],{"className":3185},[616],". Das ist falsch, das System hat ",[568,3188,837],{},". Die beiden zugehörigen Geraden sind parallel.",[559,3191,3193],{"id":3192},"typische-fehler","Typische Fehler",[3195,3196,3197,3386,3440],"ul",{},[658,3198,3199,3200,3271,3272,3329,3330,1871],{},"Die Klammer vergessen: ",[573,3201,3203,3229],{"className":3202},[576],[573,3204,3206],{"className":3205},[580],[582,3207,3208],{"xmlns":584},[586,3209,3210,3226],{},[589,3211,3212,3214,3216,3218,3220,3222,3224],{},[856,3213,858],{},[852,3215,1328],{"stretchy":1327},[856,3217,1354],{},[852,3219,854],{},[856,3221,864],{},[592,3223,633],{},[852,3225,1339],{"stretchy":1327},[596,3227,3228],{"encoding":598},"2(7 - 3y)",[573,3230,3232,3256],{"className":3231,"ariaHidden":603},[602],[573,3233,3235,3238,3241,3244,3247,3250,3253],{"className":3234},[607],[573,3236],{"className":3237,"style":1410},[611],[573,3239,858],{"className":3240},[616],[573,3242,1328],{"className":3243},[1417],[573,3245,1354],{"className":3246},[616],[573,3248],{"className":3249,"style":1157},[887],[573,3251,854],{"className":3252},[1161],[573,3254],{"className":3255,"style":1157},[887],[573,3257,3259,3262,3265,3268],{"className":3258},[607],[573,3260],{"className":3261,"style":1410},[611],[573,3263,864],{"className":3264},[616],[573,3266,633],{"className":3267,"style":649},[616,617],[573,3269,1339],{"className":3270},[1445]," ist ",[573,3273,3275,3296],{"className":3274},[576],[573,3276,3278],{"className":3277},[580],[582,3279,3280],{"xmlns":584},[586,3281,3282,3293],{},[589,3283,3284,3286,3288,3291],{},[856,3285,2264],{},[852,3287,854],{},[856,3289,3290],{},"6",[592,3292,633],{},[596,3294,3295],{"encoding":598},"14 - 6y",[573,3297,3299,3317],{"className":3298,"ariaHidden":603},[602],[573,3300,3302,3305,3308,3311,3314],{"className":3301},[607],[573,3303],{"className":3304,"style":877},[611],[573,3306,2264],{"className":3307},[616],[573,3309],{"className":3310,"style":1157},[887],[573,3312,854],{"className":3313},[1161],[573,3315],{"className":3316,"style":1157},[887],[573,3318,3320,3323,3326],{"className":3319},[607],[573,3321],{"className":3322,"style":2211},[611],[573,3324,3290],{"className":3325},[616],[573,3327,633],{"className":3328,"style":649},[616,617],", nicht ",[573,3331,3333,3353],{"className":3332},[576],[573,3334,3336],{"className":3335},[580],[582,3337,3338],{"xmlns":584},[586,3339,3340,3350],{},[589,3341,3342,3344,3346,3348],{},[856,3343,2264],{},[852,3345,854],{},[856,3347,864],{},[592,3349,633],{},[596,3351,3352],{"encoding":598},"14 - 3y",[573,3354,3356,3374],{"className":3355,"ariaHidden":603},[602],[573,3357,3359,3362,3365,3368,3371],{"className":3358},[607],[573,3360],{"className":3361,"style":877},[611],[573,3363,2264],{"className":3364},[616],[573,3366],{"className":3367,"style":1157},[887],[573,3369,854],{"className":3370},[1161],[573,3372],{"className":3373,"style":1157},[887],[573,3375,3377,3380,3383],{"className":3376},[607],[573,3378],{"className":3379,"style":2211},[611],[573,3381,864],{"className":3382},[616],[573,3384,633],{"className":3385,"style":649},[616,617],[658,3387,3388,3389,3439],{},"In dieselbe Gleichung einsetzen, aus der der Term stammt. Dann kommt immer ",[573,3390,3392,3409],{"className":3391},[576],[573,3393,3395],{"className":3394},[580],[582,3396,3397],{"xmlns":584},[586,3398,3399,3407],{},[589,3400,3401,3403,3405],{},[856,3402,925],{},[852,3404,861],{},[856,3406,925],{},[596,3408,932],{"encoding":598},[573,3410,3412,3430],{"className":3411,"ariaHidden":603},[602],[573,3413,3415,3418,3421,3424,3427],{"className":3414},[607],[573,3416],{"className":3417,"style":902},[611],[573,3419,925],{"className":3420},[616],[573,3422],{"className":3423,"style":888},[887],[573,3425,861],{"className":3426},[892],[573,3428],{"className":3429,"style":888},[887],[573,3431,3433,3436],{"className":3432},[607],[573,3434],{"className":3435,"style":902},[611],[573,3437,925],{"className":3438},[616]," heraus, obwohl das System eine eindeutige Lösung haben kann.",[658,3441,3442,3443,3471,3472,3500],{},"Nach ",[573,3444,3446,3459],{"className":3445},[576],[573,3447,3449],{"className":3448},[580],[582,3450,3451],{"xmlns":584},[586,3452,3453,3457],{},[589,3454,3455],{},[592,3456,594],{},[596,3458,594],{"encoding":598},[573,3460,3462],{"className":3461,"ariaHidden":603},[602],[573,3463,3465,3468],{"className":3464},[607],[573,3466],{"className":3467,"style":612},[611],[573,3469,594],{"className":3470},[616,617]," aufhören: Gesucht ist ein Zahlenpaar, ",[573,3473,3475,3488],{"className":3474},[576],[573,3476,3478],{"className":3477},[580],[582,3479,3480],{"xmlns":584},[586,3481,3482,3486],{},[589,3483,3484],{},[592,3485,633],{},[596,3487,633],{"encoding":598},[573,3489,3491],{"className":3490,"ariaHidden":603},[602],[573,3492,3494,3497],{"className":3493},[607],[573,3495],{"className":3496,"style":645},[611],[573,3498,633],{"className":3499,"style":649},[616,617]," muss auch berechnet werden.",{"title":3502,"searchDepth":3503,"depth":3503,"links":3504},"",2,[3505,3506,3507],{"id":561,"depth":3503,"text":562},{"id":966,"depth":3503,"text":967},{"id":3192,"depth":3503,"text":3193},[3509,3512,3515,3517,3519,3521,3524,3526,3528,3530,3532],{"lhs":3510,"rhs":3511},"a*x + b*(m*x + n)","(a + b*m)*x + b*n",{"lhs":3513,"rhs":3514},"3*x + 2*(2*x - 1)","7*x - 2",{"lhs":3513,"rhs":1059,"where":3516},{"x":3503},{"lhs":3518,"rhs":864},"2*2 - 1",{"lhs":3520,"rhs":1059},"3*2 + 2*3",{"lhs":3522,"rhs":3523},"2*(7 - 3*y) - y","14 - 7*y",{"lhs":3525,"rhs":925},"14 - 7*2",{"lhs":3527,"rhs":1024},"7 - 3*2",{"lhs":3529,"rhs":1354},"1 + 3*2",{"lhs":3531,"rhs":925},"2*1 - 2",{"lhs":3533,"rhs":3534},"4*x - 2*(2*x + 1)","-2",null,"md","substitution-method","\\begin{aligned} y &= mx + n \\\\ ax + by &= c \\end{aligned} \\quad\\Rightarrow\\quad ax + b(mx + n) = c","\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>\u003Cmtable rowspacing=\"0.25em\" columnalign=\"right left\" columnspacing=\"0em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmi>y\u003C\u002Fmi>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmrow>\u003C\u002Fmrow>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>m\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>y\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" 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