详细信息：
输入的方程组为：
 | | | | | | 249 10 | A | + | | | 131 5 | B | + | | | 211 10 | C | + | | | 81 5 | D | + | | 10 | E | + | | 5 | F | + | | 2 | G | = | | -1000 | | (1) |
| | | | 187 2 | A | + | | 65 | B | + | | 37 | C | + | | 25 | D | + | | 15 | E | + | | | 15 2 | F | + | | 4 | G | = | | 1000 | | (2) |
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解题过程：
将第 (1) 等式两边 乘以935 除以249后，可以得到等式：| | | | 187 2 | A | + | | | 24497 249 | B | + | | | 39457 498 | C | + | | | 5049 83 | D | + | | | 9350 249 | E | + | | | 4675 249 | F | + | | | 1870 249 | G | = | | - | 935000 249 | (8) |
，然后再同时用第 (2) 等式两边 减去 等式(8)两边，方程组化为：
 | | | | | | 249 10 | A | + | | | 131 5 | B | + | | | 211 10 | C | + | | | 81 5 | D | + | | 10 | E | + | | 5 | F | + | | 2 | G | = | | -1000 | | (1) |
| | - | 8312 249 | B | | - | 21031 498 | C | | - | 2974 83 | D | | - | 5615 249 | E | | - | 5615 498 | F | | - | 874 249 | G | = | | | 1184000 249 | | (2) |
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将第 (2) 等式两边 乘以32619 除以41560后，可以得到等式：| | - | 136109 5195 | B | | - | 2755061 83120 | C | | - | 584391 20780 | D | | - | 147113 8312 | E | | - | 147113 16624 | F | | - | 57247 20780 | G | = | | | 3877600 1039 | (9) |
，然后再同时用第 (1) 等式两边 加上 等式(9)两边，方程组化为：
| | | | | | 249 10 | A | | - | 1001229 83120 | C | | - | 49551 4156 | D | | - | 63993 8312 | E | | - | 63993 16624 | F | | - | 15687 20780 | G | = | | | 2838600 1039 | | (1) |
| | - | 8312 249 | B | | - | 21031 498 | C | | - | 2974 83 | D | | - | 5615 249 | E | | - | 5615 498 | F | | - | 874 249 | G | = | | | 1184000 249 | | (2) |
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将未知数的系数化为1，方程组化为：
| | | | | A | | - | 4021 8312 | C | | - | 995 2078 | D | | - | 1285 4156 | E | | - | 1285 8312 | F | | - | 63 2078 | G | = | | | 114000 1039 | | (1) |
| | | B | + | | | 21031 16624 | C | + | | | 4461 4156 | D | + | | | 5615 8312 | E | + | | | 5615 16624 | F | + | | | 437 4156 | G | = | | - | 148000 1039 | | (2) |
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所以，方程组的解为：
 | | | | A = | | | 114000 1039 | + | | | 4021 8312 | C | + | | | 995 2078 | D | + | | | 1285 4156 | E | + | | | 1285 8312 | F | + | | | 63 2078 | G |
| | B = | | - | 148000 1039 | - | | | 21031 16624 | C | - | | | 4461 4156 | D | - | | | 5615 8312 | E | - | | | 5615 16624 | F | - | | | 437 4156 | G |
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将方程组的解化为小数：
| | | | A = | | 109.720885 | + | | | 4021 8312 | C | + | | | 995 2078 | D | + | | | 1285 4156 | E | + | | | 1285 8312 | F | + | | | 63 2078 | G |
| | B = | | -142.444658 | - | | | 21031 16624 | C | - | | | 4461 4156 | D | - | | | 5615 8312 | E | - | | | 5615 16624 | F | - | | | 437 4156 | G |
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其中： C, D, E, F, G 为任意常数。
解方程组的详细方法请参阅：《多元一次方程组的解法》 |
