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Eine Variable fällt weg.",[575,706,707],{},"Nach der verbliebenen Variablen auflösen.",[575,709,710],{},"Den Wert in eine Ausgangsgleichung einsetzen und die zweite Variable berechnen.",[564,712,713,714,804,805,876,877,1127],{},"Die Formel oben zeigt den allgemeinen Fall: Erste Gleichung mal ",[579,715,717,738],{"className":716},[582],[579,718,720],{"className":719},[586],[588,721,722],{"xmlns":590},[592,723,724,735],{},[595,725,726],{},[727,728,729,731],"msub",{},[598,730,610],{},[732,733,734],"mn",{},"2",[621,736,737],{"encoding":623},"b_2",[579,739,741],{"className":740,"ariaHidden":629},[628],[579,742,744,748],{"className":743},[633],[579,745],{"className":746,"style":747},[637],"height:0.8444em;vertical-align:-0.15em;",[579,749,751,754],{"className":750},[642],[579,752,610],{"className":753},[642,643],[579,755,758],{"className":756},[757],"msupsub",[579,759,763,795],{"className":760},[761,762],"vlist-t","vlist-t2",[579,764,767,790],{"className":765},[766],"vlist-r",[579,768,772],{"className":769,"style":771},[770],"vlist","height:0.3011em;",[579,773,775,780],{"style":774},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[579,776],{"className":777,"style":779},[778],"pstrut","height:2.7em;",[579,781,787],{"className":782},[783,784,785,786],"sizing","reset-size6","size3","mtight",[579,788,734],{"className":789},[642,786],[579,791,794],{"className":792},[793],"vlist-s","​",[579,796,798],{"className":797},[766],[579,799,802],{"className":800,"style":801},[770],"height:0.15em;",[579,803],{},", zweite mal ",[579,806,808,827],{"className":807},[582],[579,809,811],{"className":810},[586],[588,812,813],{"xmlns":590},[592,814,815,824],{},[595,816,817],{},[727,818,819,821],{},[598,820,610],{},[732,822,823],{},"1",[621,825,826],{"encoding":623},"b_1",[579,828,830],{"className":829,"ariaHidden":629},[628],[579,831,833,836],{"className":832},[633],[579,834],{"className":835,"style":747},[637],[579,837,839,842],{"className":838},[642],[579,840,610],{"className":841},[642,643],[579,843,845],{"className":844},[757],[579,846,848,868],{"className":847},[761,762],[579,849,851,865],{"className":850},[766],[579,852,854],{"className":853,"style":771},[770],[579,855,856,859],{"style":774},[579,857],{"className":858,"style":779},[778],[579,860,862],{"className":861},[783,784,785,786],[579,863,823],{"className":864},[642,786],[579,866,794],{"className":867},[793],[579,869,871],{"className":870},[766],[579,872,874],{"className":873,"style":801},[770],[579,875],{},", dann subtrahieren. Ist ",[579,878,880,924],{"className":879},[582],[579,881,883],{"className":882},[586],[588,884,885],{"xmlns":590},[592,886,887,921],{},[595,888,889,895,901,904,910,916,918],{},[727,890,891,893],{},[598,892,600],{},[732,894,823],{},[727,896,897,899],{},[598,898,610],{},[732,900,734],{},[605,902,903],{},"−",[727,905,906,908],{},[598,907,600],{},[732,909,734],{},[727,911,912,914],{},[598,913,610],{},[732,915,823],{},[605,917,616],{},[732,919,920],{},"0",[621,922,923],{"encoding":623},"a_1 b_2 - a_2 b_1 = 0",[579,925,927,1022,1117],{"className":926,"ariaHidden":629},[628],[579,928,930,933,973,1013,1016,1019],{"className":929},[633],[579,931],{"className":932,"style":747},[637],[579,934,936,939],{"className":935},[642],[579,937,600],{"className":938},[642,643],[579,940,942],{"className":941},[757],[579,943,945,965],{"className":944},[761,762],[579,946,948,962],{"className":947},[766],[579,949,951],{"className":950,"style":771},[770],[579,952,953,956],{"style":774},[579,954],{"className":955,"style":779},[778],[579,957,959],{"className":958},[783,784,785,786],[579,960,823],{"className":961},[642,786],[579,963,794],{"className":964},[793],[579,966,968],{"className":967},[766],[579,969,971],{"className":970,"style":801},[770],[579,972],{},[579,974,976,979],{"className":975},[642],[579,977,610],{"className":978},[642,643],[579,980,982],{"className":981},[757],[579,983,985,1005],{"className":984},[761,762],[579,986,988,1002],{"className":987},[766],[579,989,991],{"className":990,"style":771},[770],[579,992,993,996],{"style":774},[579,994],{"className":995,"style":779},[778],[579,997,999],{"className":998},[783,784,785,786],[579,1000,734],{"className":1001},[642,786],[579,1003,794],{"className":1004},[793],[579,1006,1008],{"className":1007},[766],[579,1009,1011],{"className":1010,"style":801},[770],[579,1012],{},[579,1014],{"className":1015,"style":651},[650],[579,1017,903],{"className":1018},[655],[579,1020],{"className":1021,"style":651},[650],[579,1023,1025,1028,1068,1108,1111,1114],{"className":1024},[633],[579,1026],{"className":1027,"style":747},[637],[579,1029,1031,1034],{"className":1030},[642],[579,1032,600],{"className":1033},[642,643],[579,1035,1037],{"className":1036},[757],[579,1038,1040,1060],{"className":1039},[761,762],[579,1041,1043,1057],{"className":1042},[766],[579,1044,1046],{"className":1045,"style":771},[770],[579,1047,1048,1051],{"style":774},[579,1049],{"className":1050,"style":779},[778],[579,1052,1054],{"className":1053},[783,784,785,786],[579,1055,734],{"className":1056},[642,786],[579,1058,794],{"className":1059},[793],[579,1061,1063],{"className":1062},[766],[579,1064,1066],{"className":1065,"style":801},[770],[579,1067],{},[579,1069,1071,1074],{"className":1070},[642],[579,1072,610],{"className":1073},[642,643],[579,1075,1077],{"className":1076},[757],[579,1078,1080,1100],{"className":1079},[761,762],[579,1081,1083,1097],{"className":1082},[766],[579,1084,1086],{"className":1085,"style":771},[770],[579,1087,1088,1091],{"style":774},[579,1089],{"className":1090,"style":779},[778],[579,1092,1094],{"className":1093},[783,784,785,786],[579,1095,823],{"className":1096},[642,786],[579,1098,794],{"className":1099},[793],[579,1101,1103],{"className":1102},[766],[579,1104,1106],{"className":1105,"style":801},[770],[579,1107],{},[579,1109],{"className":1110,"style":676},[650],[579,1112,616],{"className":1113},[680],[579,1115],{"className":1116,"style":676},[650],[579,1118,1120,1124],{"className":1119},[633],[579,1121],{"className":1122,"style":1123},[637],"height:0.6444em;",[579,1125,920],{"className":1126},[642],", gibt es keine oder unendlich viele Lösungen.",[564,1129,1130],{},"Das Verfahren ist besonders praktisch, wenn keine Gleichung nach einer Variablen aufgelöst ist. In der Oberstufe wird es zum Gauß-Algorithmus erweitert.",[559,1132,1134],{"id":1133},"beispiele","Beispiele",[579,1136,1139],{"className":1137},[1138],"katex-display",[579,1140,1142,1233],{"className":1141},[582],[579,1143,1145],{"className":1144},[586],[588,1146,1148],{"xmlns":590,"display":1147},"block",[592,1149,1150,1230],{},[1151,1152,1156,1195],"mtable",{"rowspacing":1153,"columnalign":1154,"columnspacing":1155},"0.25em","right left","0em",[1157,1158,1159,1182],"mtr",{},[1160,1161,1162],"mtd",{},[1163,1164,1165],"mstyle",{"scriptlevel":920,"displaystyle":629},[595,1166,1167,1171,1173,1175,1177,1180],{},[1168,1169,1170],"mtext",{},"I:  ",[732,1172,734],{},[598,1174,603],{},[605,1176,607],{},[732,1178,1179],{},"3",[598,1181,613],{},[1160,1183,1184],{},[1163,1185,1186],{"scriptlevel":920,"displaystyle":629},[595,1187,1188,1190,1192],{},[595,1189],{},[605,1191,616],{},[732,1193,1194],{},"12",[1157,1196,1197,1217],{},[1160,1198,1199],{},[1163,1200,1201],{"scriptlevel":920,"displaystyle":629},[595,1202,1203,1206,1209,1211,1213,1215],{},[1168,1204,1205],{},"II:  ",[732,1207,1208],{},"5",[598,1210,603],{},[605,1212,903],{},[732,1214,1179],{},[598,1216,613],{},[1160,1218,1219],{},[1163,1220,1221],{"scriptlevel":920,"displaystyle":629},[595,1222,1223,1225,1227],{},[595,1224],{},[605,1226,616],{},[732,1228,1229],{},"9",[621,1231,1232],{"encoding":623},"\\begin{aligned} \\text{I:}\\ \\ 2x + 3y &= 12 \\\\ \\text{II:}\\ \\ 5x - 3y &= 9 \\end{aligned}",[579,1234,1236],{"className":1235,"ariaHidden":629},[628],[579,1237,1239,1243],{"className":1238},[633],[579,1240],{"className":1241,"style":1242},[637],"height:2.7em;vertical-align:-1.1em;",[579,1244,1246],{"className":1245},[642],[579,1247,1249,1364],{"className":1248},[1151],[579,1250,1253],{"className":1251},[1252],"col-align-r",[579,1254,1256,1355],{"className":1255},[761,762],[579,1257,1259,1352],{"className":1258},[766],[579,1260,1263,1309],{"className":1261,"style":1262},[770],"height:1.6em;",[579,1264,1266,1270],{"style":1265},"top:-3.76em;",[579,1267],{"className":1268,"style":1269},[778],"height:3em;",[579,1271,1273,1281,1285,1288,1291,1294,1297,1300,1303,1306],{"className":1272},[642],[579,1274,1277],{"className":1275},[642,1276],"text",[579,1278,1280],{"className":1279},[642],"I:",[579,1282,1284],{"className":1283},[650]," ",[579,1286,1284],{"className":1287},[650],[579,1289,734],{"className":1290},[642],[579,1292,603],{"className":1293},[642,643],[579,1295],{"className":1296,"style":651},[650],[579,1298,607],{"className":1299},[655],[579,1301],{"className":1302,"style":651},[650],[579,1304,1179],{"className":1305},[642],[579,1307,613],{"className":1308,"style":672},[642,643],[579,1310,1312,1315],{"style":1311},"top:-2.26em;",[579,1313],{"className":1314,"style":1269},[778],[579,1316,1318,1325,1328,1331,1334,1337,1340,1343,1346,1349],{"className":1317},[642],[579,1319,1321],{"className":1320},[642,1276],[579,1322,1324],{"className":1323},[642],"II:",[579,1326,1284],{"className":1327},[650],[579,1329,1284],{"className":1330},[650],[579,1332,1208],{"className":1333},[642],[579,1335,603],{"className":1336},[642,643],[579,1338],{"className":1339,"style":651},[650],[579,1341,903],{"className":1342},[655],[579,1344],{"className":1345,"style":651},[650],[579,1347,1179],{"className":1348},[642],[579,1350,613],{"className":1351,"style":672},[642,643],[579,1353,794],{"className":1354},[793],[579,1356,1358],{"className":1357},[766],[579,1359,1362],{"className":1360,"style":1361},[770],"height:1.1em;",[579,1363],{},[579,1365,1368],{"className":1366},[1367],"col-align-l",[579,1369,1371,1426],{"className":1370},[761,762],[579,1372,1374,1423],{"className":1373},[766],[579,1375,1377,1400],{"className":1376,"style":1262},[770],[579,1378,1379,1382],{"style":1265},[579,1380],{"className":1381,"style":1269},[778],[579,1383,1385,1388,1391,1394,1397],{"className":1384},[642],[579,1386],{"className":1387},[642],[579,1389],{"className":1390,"style":676},[650],[579,1392,616],{"className":1393},[680],[579,1395],{"className":1396,"style":676},[650],[579,1398,1194],{"className":1399},[642],[579,1401,1402,1405],{"style":1311},[579,1403],{"className":1404,"style":1269},[778],[579,1406,1408,1411,1414,1417,1420],{"className":1407},[642],[579,1409],{"className":1410},[642],[579,1412],{"className":1413,"style":676},[650],[579,1415,616],{"className":1416},[680],[579,1418],{"className":1419,"style":676},[650],[579,1421,1229],{"className":1422},[642],[579,1424,794],{"className":1425},[793],[579,1427,1429],{"className":1428},[766],[579,1430,1432],{"className":1431,"style":1361},[770],[579,1433],{},[564,1435,1436,1437,1466,1467,1502,1503,1537,1538,1596,1597,1648,1649,1596,1729,1780,1781,1899,1900,1968],{},"Vor ",[579,1438,1440,1453],{"className":1439},[582],[579,1441,1443],{"className":1442},[586],[588,1444,1445],{"xmlns":590},[592,1446,1447,1451],{},[595,1448,1449],{},[598,1450,613],{},[621,1452,613],{"encoding":623},[579,1454,1456],{"className":1455,"ariaHidden":629},[628],[579,1457,1459,1463],{"className":1458},[633],[579,1460],{"className":1461,"style":1462},[637],"height:0.625em;vertical-align:-0.1944em;",[579,1464,613],{"className":1465,"style":672},[642,643]," stehen schon ",[579,1468,1470,1486],{"className":1469},[582],[579,1471,1473],{"className":1472},[586],[588,1474,1475],{"xmlns":590},[592,1476,1477,1483],{},[595,1478,1479,1481],{},[605,1480,607],{},[732,1482,1179],{},[621,1484,1485],{"encoding":623},"+3",[579,1487,1489],{"className":1488,"ariaHidden":629},[628],[579,1490,1492,1496,1499],{"className":1491},[633],[579,1493],{"className":1494,"style":1495},[637],"height:0.7278em;vertical-align:-0.0833em;",[579,1497,607],{"className":1498},[642],[579,1500,1179],{"className":1501},[642]," und ",[579,1504,1506,1522],{"className":1505},[582],[579,1507,1509],{"className":1508},[586],[588,1510,1511],{"xmlns":590},[592,1512,1513,1519],{},[595,1514,1515,1517],{},[605,1516,903],{},[732,1518,1179],{},[621,1520,1521],{"encoding":623},"-3",[579,1523,1525],{"className":1524,"ariaHidden":629},[628],[579,1526,1528,1531,1534],{"className":1527},[633],[579,1529],{"className":1530,"style":1495},[637],[579,1532,903],{"className":1533},[642],[579,1535,1179],{"className":1536},[642],". Addieren: ",[579,1539,1541,1563],{"className":1540},[582],[579,1542,1544],{"className":1543},[586],[588,1545,1546],{"xmlns":590},[592,1547,1548,1560],{},[595,1549,1550,1553,1555,1557],{},[732,1551,1552],{},"7",[598,1554,603],{},[605,1556,616],{},[732,1558,1559],{},"21",[621,1561,1562],{"encoding":623},"7x = 21",[579,1564,1566,1587],{"className":1565,"ariaHidden":629},[628],[579,1567,1569,1572,1575,1578,1581,1584],{"className":1568},[633],[579,1570],{"className":1571,"style":1123},[637],[579,1573,1552],{"className":1574},[642],[579,1576,603],{"className":1577},[642,643],[579,1579],{"className":1580,"style":676},[650],[579,1582,616],{"className":1583},[680],[579,1585],{"className":1586,"style":676},[650],[579,1588,1590,1593],{"className":1589},[633],[579,1591],{"className":1592,"style":1123},[637],[579,1594,1559],{"className":1595},[642],", also ",[579,1598,1600,1618],{"className":1599},[582],[579,1601,1603],{"className":1602},[586],[588,1604,1605],{"xmlns":590},[592,1606,1607,1615],{},[595,1608,1609,1611,1613],{},[598,1610,603],{},[605,1612,616],{},[732,1614,1179],{},[621,1616,1617],{"encoding":623},"x = 3",[579,1619,1621,1639],{"className":1620,"ariaHidden":629},[628],[579,1622,1624,1627,1630,1633,1636],{"className":1623},[633],[579,1625],{"className":1626,"style":690},[637],[579,1628,603],{"className":1629},[642,643],[579,1631],{"className":1632,"style":676},[650],[579,1634,616],{"className":1635},[680],[579,1637],{"className":1638,"style":676},[650],[579,1640,1642,1645],{"className":1641},[633],[579,1643],{"className":1644,"style":1123},[637],[579,1646,1179],{"className":1647},[642],". Einsetzen in I: ",[579,1650,1652,1677],{"className":1651},[582],[579,1653,1655],{"className":1654},[586],[588,1656,1657],{"xmlns":590},[592,1658,1659,1674],{},[595,1660,1661,1664,1666,1668,1670,1672],{},[732,1662,1663],{},"6",[605,1665,607],{},[732,1667,1179],{},[598,1669,613],{},[605,1671,616],{},[732,1673,1194],{},[621,1675,1676],{"encoding":623},"6 + 3y = 12",[579,1678,1680,1698,1720],{"className":1679,"ariaHidden":629},[628],[579,1681,1683,1686,1689,1692,1695],{"className":1682},[633],[579,1684],{"className":1685,"style":1495},[637],[579,1687,1663],{"className":1688},[642],[579,1690],{"className":1691,"style":651},[650],[579,1693,607],{"className":1694},[655],[579,1696],{"className":1697,"style":651},[650],[579,1699,1701,1705,1708,1711,1714,1717],{"className":1700},[633],[579,1702],{"className":1703,"style":1704},[637],"height:0.8389em;vertical-align:-0.1944em;",[579,1706,1179],{"className":1707},[642],[579,1709,613],{"className":1710,"style":672},[642,643],[579,1712],{"className":1713,"style":676},[650],[579,1715,616],{"className":1716},[680],[579,1718],{"className":1719,"style":676},[650],[579,1721,1723,1726],{"className":1722},[633],[579,1724],{"className":1725,"style":1123},[637],[579,1727,1194],{"className":1728},[642],[579,1730,1732,1750],{"className":1731},[582],[579,1733,1735],{"className":1734},[586],[588,1736,1737],{"xmlns":590},[592,1738,1739,1747],{},[595,1740,1741,1743,1745],{},[598,1742,613],{},[605,1744,616],{},[732,1746,734],{},[621,1748,1749],{"encoding":623},"y = 2",[579,1751,1753,1771],{"className":1752,"ariaHidden":629},[628],[579,1754,1756,1759,1762,1765,1768],{"className":1755},[633],[579,1757],{"className":1758,"style":1462},[637],[579,1760,613],{"className":1761,"style":672},[642,643],[579,1763],{"className":1764,"style":676},[650],[579,1766,616],{"className":1767},[680],[579,1769],{"className":1770,"style":676},[650],[579,1772,1774,1777],{"className":1773},[633],[579,1775],{"className":1776,"style":1123},[637],[579,1778,734],{"className":1779},[642],". Probe in II: ",[579,1782,1784,1815],{"className":1783},[582],[579,1785,1787],{"className":1786},[586],[588,1788,1789],{"xmlns":590},[592,1790,1791,1812],{},[595,1792,1793,1795,1798,1800,1802,1804,1806,1808,1810],{},[732,1794,1208],{},[605,1796,1797],{},"⋅",[732,1799,1179],{},[605,1801,903],{},[732,1803,1179],{},[605,1805,1797],{},[732,1807,734],{},[605,1809,616],{},[732,1811,1229],{},[621,1813,1814],{"encoding":623},"5 \\cdot 3 - 3 \\cdot 2 = 9",[579,1816,1818,1836,1854,1872,1890],{"className":1817,"ariaHidden":629},[628],[579,1819,1821,1824,1827,1830,1833],{"className":1820},[633],[579,1822],{"className":1823,"style":1123},[637],[579,1825,1208],{"className":1826},[642],[579,1828],{"className":1829,"style":651},[650],[579,1831,1797],{"className":1832},[655],[579,1834],{"className":1835,"style":651},[650],[579,1837,1839,1842,1845,1848,1851],{"className":1838},[633],[579,1840],{"className":1841,"style":1495},[637],[579,1843,1179],{"className":1844},[642],[579,1846],{"className":1847,"style":651},[650],[579,1849,903],{"className":1850},[655],[579,1852],{"className":1853,"style":651},[650],[579,1855,1857,1860,1863,1866,1869],{"className":1856},[633],[579,1858],{"className":1859,"style":1123},[637],[579,1861,1179],{"className":1862},[642],[579,1864],{"className":1865,"style":651},[650],[579,1867,1797],{"className":1868},[655],[579,1870],{"className":1871,"style":651},[650],[579,1873,1875,1878,1881,1884,1887],{"className":1874},[633],[579,1876],{"className":1877,"style":1123},[637],[579,1879,734],{"className":1880},[642],[579,1882],{"className":1883,"style":676},[650],[579,1885,616],{"className":1886},[680],[579,1888],{"className":1889,"style":676},[650],[579,1891,1893,1896],{"className":1892},[633],[579,1894],{"className":1895,"style":1123},[637],[579,1897,1229],{"className":1898},[642],". Lösung ",[579,1901,1903,1929],{"className":1902},[582],[579,1904,1906],{"className":1905},[586],[588,1907,1908],{"xmlns":590},[592,1909,1910,1926],{},[595,1911,1912,1916,1918,1921,1923],{},[605,1913,1915],{"stretchy":1914},"false","(",[732,1917,1179],{},[605,1919,1920],{},"∣",[732,1922,734],{},[605,1924,1925],{"stretchy":1914},")",[621,1927,1928],{"encoding":623},"(3 \\mid 2)",[579,1930,1932,1955],{"className":1931,"ariaHidden":629},[628],[579,1933,1935,1939,1943,1946,1949,1952],{"className":1934},[633],[579,1936],{"className":1937,"style":1938},[637],"height:1em;vertical-align:-0.25em;",[579,1940,1915],{"className":1941},[1942],"mopen",[579,1944,1179],{"className":1945},[642],[579,1947],{"className":1948,"style":676},[650],[579,1950,1920],{"className":1951},[680],[579,1953],{"className":1954,"style":676},[650],[579,1956,1958,1961,1964],{"className":1957},[633],[579,1959],{"className":1960,"style":1938},[637],[579,1962,734],{"className":1963},[642],[579,1965,1925],{"className":1966},[1967],"mclose",".",[564,1970,1971],{},"Hier muss erst multipliziert werden:",[579,1973,1975],{"className":1974},[1138],[579,1976,1978,2073],{"className":1977},[582],[579,1979,1981],{"className":1980},[586],[588,1982,1983],{"xmlns":590,"display":1147},[592,1984,1985,2070],{},[1151,1986,1987,2029],{"rowspacing":1153,"columnalign":1154,"columnspacing":1155},[1157,1988,1989,2007],{},[1160,1990,1991],{},[1163,1992,1993],{"scriptlevel":920,"displaystyle":629},[595,1994,1995,1997,1999,2001,2003,2005],{},[1168,1996,1170],{},[732,1998,1179],{},[598,2000,603],{},[605,2002,607],{},[732,2004,734],{},[598,2006,613],{},[1160,2008,2009],{},[1163,2010,2011],{"scriptlevel":920,"displaystyle":629},[595,2012,2013,2015,2017,2019,2022,2025,2027],{},[595,2014],{},[605,2016,616],{},[732,2018,1552],{},[650,2020],{"width":2021},"1em",[598,2023,1920],{"mathvariant":2024},"normal",[605,2026,1797],{},[732,2028,1208],{},[1157,2030,2031,2050],{},[1160,2032,2033],{},[1163,2034,2035],{"scriptlevel":920,"displaystyle":629},[595,2036,2037,2039,2042,2044,2046,2048],{},[1168,2038,1205],{},[732,2040,2041],{},"4",[598,2043,603],{},[605,2045,607],{},[732,2047,1208],{},[598,2049,613],{},[1160,2051,2052],{},[1163,2053,2054],{"scriptlevel":920,"displaystyle":629},[595,2055,2056,2058,2060,2062,2064,2066,2068],{},[595,2057],{},[605,2059,616],{},[732,2061,1552],{},[650,2063],{"width":2021},[598,2065,1920],{"mathvariant":2024},[605,2067,1797],{},[732,2069,734],{},[621,2071,2072],{"encoding":623},"\\begin{aligned} \\text{I:}\\ \\ 3x + 2y &= 7 \\quad | \\cdot 5 \\\\ \\text{II:}\\ \\ 4x + 5y &= 7 \\quad | \\cdot 2 \\end{aligned}",[579,2074,2076],{"className":2075,"ariaHidden":629},[628],[579,2077,2079,2082],{"className":2078},[633],[579,2080],{"className":2081,"style":1242},[637],[579,2083,2085],{"className":2084},[642],[579,2086,2088,2193],{"className":2087},[1151],[579,2089,2091],{"className":2090},[1252],[579,2092,2094,2185],{"className":2093},[761,762],[579,2095,2097,2182],{"className":2096},[766],[579,2098,2100,2141],{"className":2099,"style":1262},[770],[579,2101,2102,2105],{"style":1265},[579,2103],{"className":2104,"style":1269},[778],[579,2106,2108,2114,2117,2120,2123,2126,2129,2132,2135,2138],{"className":2107},[642],[579,2109,2111],{"className":2110},[642,1276],[579,2112,1280],{"className":2113},[642],[579,2115,1284],{"className":2116},[650],[579,2118,1284],{"className":2119},[650],[579,2121,1179],{"className":2122},[642],[579,2124,603],{"className":2125},[642,643],[579,2127],{"className":2128,"style":651},[650],[579,2130,607],{"className":2131},[655],[579,2133],{"className":2134,"style":651},[650],[579,2136,734],{"className":2137},[642],[579,2139,613],{"className":2140,"style":672},[642,643],[579,2142,2143,2146],{"style":1311},[579,2144],{"className":2145,"style":1269},[778],[579,2147,2149,2155,2158,2161,2164,2167,2170,2173,2176,2179],{"className":2148},[642],[579,2150,2152],{"className":2151},[642,1276],[579,2153,1324],{"className":2154},[642],[579,2156,1284],{"className":2157},[650],[579,2159,1284],{"className":2160},[650],[579,2162,2041],{"className":2163},[642],[579,2165,603],{"className":2166},[642,643],[579,2168],{"className":2169,"style":651},[650],[579,2171,607],{"className":2172},[655],[579,2174],{"className":2175,"style":651},[650],[579,2177,1208],{"className":2178},[642],[579,2180,613],{"className":2181,"style":672},[642,643],[579,2183,794],{"className":2184},[793],[579,2186,2188],{"className":2187},[766],[579,2189,2191],{"className":2190,"style":1361},[770],[579,2192],{},[579,2194,2196],{"className":2195},[1367],[579,2197,2199,2291],{"className":2198},[761,762],[579,2200,2202,2288],{"className":2201},[766],[579,2203,2205,2247],{"className":2204,"style":1262},[770],[579,2206,2207,2210],{"style":1265},[579,2208],{"className":2209,"style":1269},[778],[579,2211,2213,2216,2219,2222,2225,2228,2232,2235,2238,2241,2244],{"className":2212},[642],[579,2214],{"className":2215},[642],[579,2217],{"className":2218,"style":676},[650],[579,2220,616],{"className":2221},[680],[579,2223],{"className":2224,"style":676},[650],[579,2226,1552],{"className":2227},[642],[579,2229],{"className":2230,"style":2231},[650],"margin-right:1em;",[579,2233,1920],{"className":2234},[642],[579,2236],{"className":2237,"style":651},[650],[579,2239,1797],{"className":2240},[655],[579,2242],{"className":2243,"style":651},[650],[579,2245,1208],{"className":2246},[642],[579,2248,2249,2252],{"style":1311},[579,2250],{"className":2251,"style":1269},[778],[579,2253,2255,2258,2261,2264,2267,2270,2273,2276,2279,2282,2285],{"className":2254},[642],[579,2256],{"className":2257},[642],[579,2259],{"className":2260,"style":676},[650],[579,2262,616],{"className":2263},[680],[579,2265],{"className":2266,"style":676},[650],[579,2268,1552],{"className":2269},[642],[579,2271],{"className":2272,"style":2231},[650],[579,2274,1920],{"className":2275},[642],[579,2277],{"className":2278,"style":651},[650],[579,2280,1797],{"className":2281},[655],[579,2283],{"className":2284,"style":651},[650],[579,2286,734],{"className":2287},[642],[579,2289,794],{"className":2290},[793],[579,2292,2294],{"className":2293},[766],[579,2295,2297],{"className":2296,"style":1361},[770],[579,2298],{},[564,2300,2301,2302,1502,2388,2473],{},"Das ergibt ",[579,2303,2305,2334],{"className":2304},[582],[579,2306,2308],{"className":2307},[586],[588,2309,2310],{"xmlns":590},[592,2311,2312,2331],{},[595,2313,2314,2317,2319,2321,2324,2326,2328],{},[732,2315,2316],{},"15",[598,2318,603],{},[605,2320,607],{},[732,2322,2323],{},"10",[598,2325,613],{},[605,2327,616],{},[732,2329,2330],{},"35",[621,2332,2333],{"encoding":623},"15x + 10y = 35",[579,2335,2337,2358,2379],{"className":2336,"ariaHidden":629},[628],[579,2338,2340,2343,2346,2349,2352,2355],{"className":2339},[633],[579,2341],{"className":2342,"style":1495},[637],[579,2344,2316],{"className":2345},[642],[579,2347,603],{"className":2348},[642,643],[579,2350],{"className":2351,"style":651},[650],[579,2353,607],{"className":2354},[655],[579,2356],{"className":2357,"style":651},[650],[579,2359,2361,2364,2367,2370,2373,2376],{"className":2360},[633],[579,2362],{"className":2363,"style":1704},[637],[579,2365,2323],{"className":2366},[642],[579,2368,613],{"className":2369,"style":672},[642,643],[579,2371],{"className":2372,"style":676},[650],[579,2374,616],{"className":2375},[680],[579,2377],{"className":2378,"style":676},[650],[579,2380,2382,2385],{"className":2381},[633],[579,2383],{"className":2384,"style":1123},[637],[579,2386,2330],{"className":2387},[642],[579,2389,2391,2419],{"className":2390},[582],[579,2392,2394],{"className":2393},[586],[588,2395,2396],{"xmlns":590},[592,2397,2398,2416],{},[595,2399,2400,2403,2405,2407,2409,2411,2413],{},[732,2401,2402],{},"8",[598,2404,603],{},[605,2406,607],{},[732,2408,2323],{},[598,2410,613],{},[605,2412,616],{},[732,2414,2415],{},"14",[621,2417,2418],{"encoding":623},"8x + 10y = 14",[579,2420,2422,2443,2464],{"className":2421,"ariaHidden":629},[628],[579,2423,2425,2428,2431,2434,2437,2440],{"className":2424},[633],[579,2426],{"className":2427,"style":1495},[637],[579,2429,2402],{"className":2430},[642],[579,2432,603],{"className":2433},[642,643],[579,2435],{"className":2436,"style":651},[650],[579,2438,607],{"className":2439},[655],[579,2441],{"className":2442,"style":651},[650],[579,2444,2446,2449,2452,2455,2458,2461],{"className":2445},[633],[579,2447],{"className":2448,"style":1704},[637],[579,2450,2323],{"className":2451},[642],[579,2453,613],{"className":2454,"style":672},[642,643],[579,2456],{"className":2457,"style":676},[650],[579,2459,616],{"className":2460},[680],[579,2462],{"className":2463,"style":676},[650],[579,2465,2467,2470],{"className":2466},[633],[579,2468],{"className":2469,"style":1123},[637],[579,2471,2415],{"className":2472},[642],". Subtrahieren:",[579,2475,2477],{"className":2476},[1138],[579,2478,2480,2514],{"className":2479},[582],[579,2481,2483],{"className":2482},[586],[588,2484,2485],{"xmlns":590,"display":1147},[592,2486,2487,2511],{},[595,2488,2489,2491,2493,2495,2497,2500,2503,2505,2507,2509],{},[732,2490,1552],{},[598,2492,603],{},[605,2494,616],{},[732,2496,1559],{},[1168,2498,2499],{},"  ",[605,2501,2502],{},"⇒",[1168,2504,2499],{},[598,2506,603],{},[605,2508,616],{},[732,2510,1179],{},[621,2512,2513],{"encoding":623},"7x = 21 \\;\\Rightarrow\\; x = 3",[579,2515,2517,2538,2562,2580],{"className":2516,"ariaHidden":629},[628],[579,2518,2520,2523,2526,2529,2532,2535],{"className":2519},[633],[579,2521],{"className":2522,"style":1123},[637],[579,2524,1552],{"className":2525},[642],[579,2527,603],{"className":2528},[642,643],[579,2530],{"className":2531,"style":676},[650],[579,2533,616],{"className":2534},[680],[579,2536],{"className":2537,"style":676},[650],[579,2539,2541,2544,2547,2550,2553,2556,2559],{"className":2540},[633],[579,2542],{"className":2543,"style":1123},[637],[579,2545,1559],{"className":2546},[642],[579,2548],{"className":2549,"style":676},[650],[579,2551],{"className":2552,"style":676},[650],[579,2554,2502],{"className":2555},[680],[579,2557],{"className":2558,"style":676},[650],[579,2560],{"className":2561,"style":676},[650],[579,2563,2565,2568,2571,2574,2577],{"className":2564},[633],[579,2566],{"className":2567,"style":690},[637],[579,2569,603],{"className":2570},[642,643],[579,2572],{"className":2573,"style":676},[650],[579,2575,616],{"className":2576},[680],[579,2578],{"className":2579,"style":676},[650],[579,2581,2583,2586],{"className":2582},[633],[579,2584],{"className":2585,"style":1123},[637],[579,2587,1179],{"className":2588},[642],[564,2590,2591,2592,1596,2670,1780,2726,1899,2858,1968],{},"Einsetzen in I: ",[579,2593,2595,2619],{"className":2594},[582],[579,2596,2598],{"className":2597},[586],[588,2599,2600],{"xmlns":590},[592,2601,2602,2616],{},[595,2603,2604,2606,2608,2610,2612,2614],{},[732,2605,1229],{},[605,2607,607],{},[732,2609,734],{},[598,2611,613],{},[605,2613,616],{},[732,2615,1552],{},[621,2617,2618],{"encoding":623},"9 + 2y = 7",[579,2620,2622,2640,2661],{"className":2621,"ariaHidden":629},[628],[579,2623,2625,2628,2631,2634,2637],{"className":2624},[633],[579,2626],{"className":2627,"style":1495},[637],[579,2629,1229],{"className":2630},[642],[579,2632],{"className":2633,"style":651},[650],[579,2635,607],{"className":2636},[655],[579,2638],{"className":2639,"style":651},[650],[579,2641,2643,2646,2649,2652,2655,2658],{"className":2642},[633],[579,2644],{"className":2645,"style":1704},[637],[579,2647,734],{"className":2648},[642],[579,2650,613],{"className":2651,"style":672},[642,643],[579,2653],{"className":2654,"style":676},[650],[579,2656,616],{"className":2657},[680],[579,2659],{"className":2660,"style":676},[650],[579,2662,2664,2667],{"className":2663},[633],[579,2665],{"className":2666,"style":1123},[637],[579,2668,1552],{"className":2669},[642],[579,2671,2673,2693],{"className":2672},[582],[579,2674,2676],{"className":2675},[586],[588,2677,2678],{"xmlns":590},[592,2679,2680,2690],{},[595,2681,2682,2684,2686,2688],{},[598,2683,613],{},[605,2685,616],{},[605,2687,903],{},[732,2689,823],{},[621,2691,2692],{"encoding":623},"y = -1",[579,2694,2696,2714],{"className":2695,"ariaHidden":629},[628],[579,2697,2699,2702,2705,2708,2711],{"className":2698},[633],[579,2700],{"className":2701,"style":1462},[637],[579,2703,613],{"className":2704,"style":672},[642,643],[579,2706],{"className":2707,"style":676},[650],[579,2709,616],{"className":2710},[680],[579,2712],{"className":2713,"style":676},[650],[579,2715,2717,2720,2723],{"className":2716},[633],[579,2718],{"className":2719,"style":1495},[637],[579,2721,903],{"className":2722},[642],[579,2724,823],{"className":2725},[642],[579,2727,2729,2765],{"className":2728},[582],[579,2730,2732],{"className":2731},[586],[588,2733,2734],{"xmlns":590},[592,2735,2736,2762],{},[595,2737,2738,2740,2742,2744,2746,2748,2750,2752,2754,2756,2758,2760],{},[732,2739,2041],{},[605,2741,1797],{},[732,2743,1179],{},[605,2745,607],{},[732,2747,1208],{},[605,2749,1797],{},[605,2751,1915],{"stretchy":1914},[605,2753,903],{},[732,2755,823],{},[605,2757,1925],{"stretchy":1914},[605,2759,616],{},[732,2761,1552],{},[621,2763,2764],{"encoding":623},"4 \\cdot 3 + 5 \\cdot (-1) = 7",[579,2766,2768,2786,2804,2822,2849],{"className":2767,"ariaHidden":629},[628],[579,2769,2771,2774,2777,2780,2783],{"className":2770},[633],[579,2772],{"className":2773,"style":1123},[637],[579,2775,2041],{"className":2776},[642],[579,2778],{"className":2779,"style":651},[650],[579,2781,1797],{"className":2782},[655],[579,2784],{"className":2785,"style":651},[650],[579,2787,2789,2792,2795,2798,2801],{"className":2788},[633],[579,2790],{"className":2791,"style":1495},[637],[579,2793,1179],{"className":2794},[642],[579,2796],{"className":2797,"style":651},[650],[579,2799,607],{"className":2800},[655],[579,2802],{"className":2803,"style":651},[650],[579,2805,2807,2810,2813,2816,2819],{"className":2806},[633],[579,2808],{"className":2809,"style":1123},[637],[579,2811,1208],{"className":2812},[642],[579,2814],{"className":2815,"style":651},[650],[579,2817,1797],{"className":2818},[655],[579,2820],{"className":2821,"style":651},[650],[579,2823,2825,2828,2831,2834,2837,2840,2843,2846],{"className":2824},[633],[579,2826],{"className":2827,"style":1938},[637],[579,2829,1915],{"className":2830},[1942],[579,2832,903],{"className":2833},[642],[579,2835,823],{"className":2836},[642],[579,2838,1925],{"className":2839},[1967],[579,2841],{"className":2842,"style":676},[650],[579,2844,616],{"className":2845},[680],[579,2847],{"className":2848,"style":676},[650],[579,2850,2852,2855],{"className":2851},[633],[579,2853],{"className":2854,"style":1123},[637],[579,2856,1552],{"className":2857},[642],[579,2859,2861,2885],{"className":2860},[582],[579,2862,2864],{"className":2863},[586],[588,2865,2866],{"xmlns":590},[592,2867,2868,2882],{},[595,2869,2870,2872,2874,2876,2878,2880],{},[605,2871,1915],{"stretchy":1914},[732,2873,1179],{},[605,2875,1920],{},[605,2877,903],{},[732,2879,823],{},[605,2881,1925],{"stretchy":1914},[621,2883,2884],{"encoding":623},"(3 \\mid -1)",[579,2886,2888,2909],{"className":2887,"ariaHidden":629},[628],[579,2889,2891,2894,2897,2900,2903,2906],{"className":2890},[633],[579,2892],{"className":2893,"style":1938},[637],[579,2895,1915],{"className":2896},[1942],[579,2898,1179],{"className":2899},[642],[579,2901],{"className":2902,"style":676},[650],[579,2904,1920],{"className":2905},[680],[579,2907],{"className":2908,"style":676},[650],[579,2910,2912,2915,2918,2921],{"className":2911},[633],[579,2913],{"className":2914,"style":1938},[637],[579,2916,903],{"className":2917},[642],[579,2919,823],{"className":2920},[642],[579,2922,1925],{"className":2923},[1967],[559,2925,2927],{"id":2926},"typische-fehler","Typische Fehler",[2929,2930,2931,3213,3216],"ul",{},[575,2932,2933,2934,3017,3018,3046,3047,3129,3130,1968],{},"Nur die linke Seite multiplizieren: Aus ",[579,2935,2937,2963],{"className":2936},[582],[579,2938,2940],{"className":2939},[586],[588,2941,2942],{"xmlns":590},[592,2943,2944,2960],{},[595,2945,2946,2948,2950,2952,2954,2956,2958],{},[732,2947,1179],{},[598,2949,603],{},[605,2951,607],{},[732,2953,734],{},[598,2955,613],{},[605,2957,616],{},[732,2959,1552],{},[621,2961,2962],{"encoding":623},"3x + 2y = 7",[579,2964,2966,2987,3008],{"className":2965,"ariaHidden":629},[628],[579,2967,2969,2972,2975,2978,2981,2984],{"className":2968},[633],[579,2970],{"className":2971,"style":1495},[637],[579,2973,1179],{"className":2974},[642],[579,2976,603],{"className":2977},[642,643],[579,2979],{"className":2980,"style":651},[650],[579,2982,607],{"className":2983},[655],[579,2985],{"className":2986,"style":651},[650],[579,2988,2990,2993,2996,2999,3002,3005],{"className":2989},[633],[579,2991],{"className":2992,"style":1704},[637],[579,2994,734],{"className":2995},[642],[579,2997,613],{"className":2998,"style":672},[642,643],[579,3000],{"className":3001,"style":676},[650],[579,3003,616],{"className":3004},[680],[579,3006],{"className":3007,"style":676},[650],[579,3009,3011,3014],{"className":3010},[633],[579,3012],{"className":3013,"style":1123},[637],[579,3015,1552],{"className":3016},[642]," wird mal ",[579,3019,3021,3034],{"className":3020},[582],[579,3022,3024],{"className":3023},[586],[588,3025,3026],{"xmlns":590},[592,3027,3028,3032],{},[595,3029,3030],{},[732,3031,1208],{},[621,3033,1208],{"encoding":623},[579,3035,3037],{"className":3036,"ariaHidden":629},[628],[579,3038,3040,3043],{"className":3039},[633],[579,3041],{"className":3042,"style":1123},[637],[579,3044,1208],{"className":3045},[642]," die Gleichung ",[579,3048,3050,3075],{"className":3049},[582],[579,3051,3053],{"className":3052},[586],[588,3054,3055],{"xmlns":590},[592,3056,3057,3073],{},[595,3058,3059,3061,3063,3065,3067,3069,3071],{},[732,3060,2316],{},[598,3062,603],{},[605,3064,607],{},[732,3066,2323],{},[598,3068,613],{},[605,3070,616],{},[732,3072,2330],{},[621,3074,2333],{"encoding":623},[579,3076,3078,3099,3120],{"className":3077,"ariaHidden":629},[628],[579,3079,3081,3084,3087,3090,3093,3096],{"className":3080},[633],[579,3082],{"className":3083,"style":1495},[637],[579,3085,2316],{"className":3086},[642],[579,3088,603],{"className":3089},[642,643],[579,3091],{"className":3092,"style":651},[650],[579,3094,607],{"className":3095},[655],[579,3097],{"className":3098,"style":651},[650],[579,3100,3102,3105,3108,3111,3114,3117],{"className":3101},[633],[579,3103],{"className":3104,"style":1704},[637],[579,3106,2323],{"className":3107},[642],[579,3109,613],{"className":3110,"style":672},[642,643],[579,3112],{"className":3113,"style":676},[650],[579,3115,616],{"className":3116},[680],[579,3118],{"className":3119,"style":676},[650],[579,3121,3123,3126],{"className":3122},[633],[579,3124],{"className":3125,"style":1123},[637],[579,3127,2330],{"className":3128},[642],", nicht ",[579,3131,3133,3159],{"className":3132},[582],[579,3134,3136],{"className":3135},[586],[588,3137,3138],{"xmlns":590},[592,3139,3140,3156],{},[595,3141,3142,3144,3146,3148,3150,3152,3154],{},[732,3143,2316],{},[598,3145,603],{},[605,3147,607],{},[732,3149,2323],{},[598,3151,613],{},[605,3153,616],{},[732,3155,1552],{},[621,3157,3158],{"encoding":623},"15x + 10y = 7",[579,3160,3162,3183,3204],{"className":3161,"ariaHidden":629},[628],[579,3163,3165,3168,3171,3174,3177,3180],{"className":3164},[633],[579,3166],{"className":3167,"style":1495},[637],[579,3169,2316],{"className":3170},[642],[579,3172,603],{"className":3173},[642,643],[579,3175],{"className":3176,"style":651},[650],[579,3178,607],{"className":3179},[655],[579,3181],{"className":3182,"style":651},[650],[579,3184,3186,3189,3192,3195,3198,3201],{"className":3185},[633],[579,3187],{"className":3188,"style":1704},[637],[579,3190,2323],{"className":3191},[642],[579,3193,613],{"className":3194,"style":672},[642,643],[579,3196],{"className":3197,"style":676},[650],[579,3199,616],{"className":3200},[680],[579,3202],{"className":3203,"style":676},[650],[579,3205,3207,3210],{"className":3206},[633],[579,3208],{"className":3209,"style":1123},[637],[579,3211,1552],{"className":3212},[642],[575,3214,3215],{},"Beim Subtrahieren die Vorzeichen falsch behandeln: Jeder Summand der zweiten Gleichung wird abgezogen, auch die rechte Seite.",[575,3217,3218],{},"Addieren, obwohl die Zahlen gleich (statt entgegengesetzt) sind. Dann verdoppelt sich die Variable, statt wegzufallen; man muss subtrahieren.",{"title":3220,"searchDepth":3221,"depth":3221,"links":3222},"",2,[3223,3224,3225],{"id":561,"depth":3221,"text":562},{"id":1133,"depth":3221,"text":1134},{"id":2926,"depth":3221,"text":2927},[3227,3230,3233,3235,3237,3239,3241,3243,3245,3248,3250],{"lhs":3228,"rhs":3229},"(a1*x + b1*y)*b2 - (a2*x + b2*y)*b1","(a1*b2 - a2*b1)*x",{"lhs":3231,"rhs":3232},"(2*x + 3*y) + (5*x - 3*y)","7*x",{"lhs":3234,"rhs":1559},"12 + 9",{"lhs":3236,"rhs":734},"(12 - 2*3)\u002F3",{"lhs":3238,"rhs":1194},"2*3 + 3*2",{"lhs":3240,"rhs":1229},"5*3 - 3*2",{"lhs":3242,"rhs":3232},"5*(3*x + 2*y) - 2*(4*x + 5*y)",{"lhs":3244,"rhs":1559},"5*7 - 2*7",{"lhs":3246,"rhs":3247},"(7 - 3*3)\u002F2","-1",{"lhs":3249,"rhs":1552},"3*3 + 2*(-1)",{"lhs":3251,"rhs":1552},"4*3 + 5*(-1)",null,"md","elimination-method","\\begin{aligned} a_1 x + b_1 y &= c_1 \\ \\ | \\cdot b_2 \\\\ a_2 x + b_2 y &= c_2 \\ \\ | \\cdot b_1 \\end{aligned} \\quad\\Rightarrow\\quad (a_1 b_2 - a_2 b_1)\\,x = c_1 b_2 - c_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>\u003Cmtable rowspacing=\"0.25em\" columnalign=\"right left\" columnspacing=\"0em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\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>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmrow>\u003C\u002Fmrow>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\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>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmrow>\u003C\u002Fmrow>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cmspace width=\"1em\"\u002F>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\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 stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\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>\u003Cannotation encoding=\"application\u002Fx-tex\">\\begin{aligned} a_1 x + b_1 y &= c_1 \\ \\ | \\cdot b_2 \\\\ a_2 x + b_2 y &= c_2 \\ \\ | \\cdot b_1 \\end{aligned} \\quad\\Rightarrow\\quad (a_1 b_2 - a_2 b_1)\\,x = c_1 b_2 - c_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:2.7em;vertical-align:-1.1em;\">\u003C\u002Fspan>\u003Cspan 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