详细信息: 输入的方程组为:
 | | | | | 2 | A | + | | 3 | B | + | | 4 | C | + | | 3 | D | | -2 | E | = | | 5 | | (1) |
| | | 5 | A | + | | 4 | B | + | | 3 | C | + | | 4 | D | + | | 9 | E | = | | 2 | | (2) |
| | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (3) |
| | | 解题过程:
将第 (1) 等式两边 乘以5 除以2后,可以得到等式:| | | 5 | A | + | | | 15 2 | B | + | | 10 | C | + | | | 15 2 | D | | -5 | E | = | | | 25 2 | (6) | ,然后再同时用第 (2) 等式两边 减去 等式(6)两边,方程组化为:
 | | | | | 2 | A | + | | 3 | B | + | | 4 | C | + | | 3 | D | | -2 | E | = | | 5 | | (1) |
| | - | 7 2 | B | | -7 | C | | - | 7 2 | D | + | | 14 | E | = | | - | 21 2 | | (2) |
| | | A | + | | B | + | | C | + | | D | + | | E | = | | 1 | | (3) |
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将第 (1) 等式两边 除以2后,可以得到等式:| | | A | + | | | 3 2 | B | + | | 2 | C | + | | | 3 2 | D | | -1 | E | = | | | 5 2 | (7) | ,然后再同时用第 (3) 等式两边 减去 等式(7)两边,方程组化为:
 | | | | | 2 | A | + | | 3 | B | + | | 4 | C | + | | 3 | D | | -2 | E | = | | 5 | | (1) |
| | - | 7 2 | B | | -7 | C | | - | 7 2 | D | + | | 14 | E | = | | - | 21 2 | | (2) |
| | - | 1 2 | B | | -1 | C | | - | 1 2 | D | + | | 2 | E | = | | - | 3 2 | | (3) |
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将第 (2) 等式两边 除以7后,可以得到等式:| | - | 1 2 | B | | -1 | C | | - | 1 2 | D | + | | 2 | E | = | | - | 3 2 | (8) | ,然后再同时用第 (3) 等式两边 减去 等式(8)两边,方程组化为:
 | | | | | 2 | A | + | | 3 | B | + | | 4 | C | + | | 3 | D | | -2 | E | = | | 5 | | (1) |
| | - | 7 2 | B | | -7 | C | | - | 7 2 | D | + | | 14 | E | = | | - | 21 2 | | (2) |
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将第 (2) 等式两边 乘以2 除以7后,可以得到等式:| | -1 | B | | -2 | C | | -1 | D | + | | 4 | E | = | | -3 | (9) | ,然后再同时用第 (4) 等式两边 加上 等式(9)两边,方程组化为:
 | | | | | 2 | A | + | | 3 | B | + | | 4 | C | + | | 3 | D | | -2 | E | = | | 5 | | (1) |
| | - | 7 2 | B | | -7 | C | | - | 7 2 | D | + | | 14 | E | = | | - | 21 2 | | (2) |
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将第 (2) 等式两边 乘以6 除以7后,可以得到等式:| | -3 | B | | -6 | C | | -3 | D | + | | 12 | E | = | | -9 | (10) | ,然后再同时用第 (1) 等式两边 加上 等式(10)两边,方程组化为:
 | | | | | - | 7 2 | B | | -7 | C | | - | 7 2 | D | + | | 14 | E | = | | - | 21 2 | | (2) |
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将未知数的系数化为1,方程组化为:
所以,方程组的解为:
其中: C, D, E 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》 |