详细信息: 输入的方程组为:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | = | | 200 | | (1) |
| | A | + | | B | + | | C | + | | D | + | | F | + | | G | + | | H | = | | 200 | | (2) |
| | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | = | | 200 | | (3) |
| | | | | | 解题过程:
用第 (2) 式两边同时 减去 第 (1) 等式两边,方程组化为:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | = | | 200 | | (1) |
| | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | = | | 200 | | (3) |
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用第 (3) 式两边同时 减去 第 (1) 等式两边,方程组化为:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | = | | 200 | | (1) |
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用第 (1) 式两边同时 加上 第 (2) 等式两边,方程组化为:
| | | | A | + | | B | + | | C | + | | D | + | | F | + | | G | + | | H | = | | 200 | | (1) |
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将未知数的系数化为1,方程组化为:
| | | | A | + | | B | + | | C | + | | D | + | | F | + | | G | + | | H | = | | 200 | | (1) |
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所以,方程组的解为:
| | | A = | | 200 | - | | 1 | B | - | | 1 | C | - | | 1 | D | - | | 1 | F | - | | 1 | G | - | | 1 | H |
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其中: B, C, D, F, G, H 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》 |