detailed information: The input equation set is:
 | | | | A | + | | B | + | | C | + | | D | + | | E | + | | | 321 2 | F | = | | 0 | | (1) |
| | | 89 20 | A | + | | | 193 20 | B | + | | | 273 20 | C | + | | | 113 20 | D | + | | | 43 5 | E | + | | 65 | F | + | | | 23 5 | G | = | | | 6458 5 | | (2) |
| | | | | | Question solving process:
Multiply both sides of equation (1) by 89 Divide the two sides of equation (1) by 20, the equation can be obtained: | | | 89 20 | A | + | | | 89 20 | B | + | | | 89 20 | C | + | | | 89 20 | D | + | | | 89 20 | E | + | | | 28569 40 | F | = | | 0 | (8) | , then subtract both sides of equation (8) from both sides of equation (2), the equations are reduced to:
 | | | | A | + | | B | + | | C | + | | D | + | | E | + | | | 321 2 | F | = | | 0 | | (1) |
| | | 26 5 | B | + | | | 46 5 | C | + | | | 6 5 | D | + | | | 83 20 | E | | - | 25969 40 | F | + | | | 23 5 | G | = | | | 6458 5 | | (2) |
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Multiply both sides of equation (2) by 5 Divide both sides of equation (2) by 26, get the equation: | | B | + | | | 23 13 | C | + | | | 3 13 | D | + | | | 83 104 | E | | - | 25969 208 | F | + | | | 23 26 | G | = | | | 3229 13 | (9) | , then subtract both sides of equation (9) from both sides of equation (1), get the equation:
 | | | | A | | - | 10 13 | C | + | | | 10 13 | D | + | | | 21 104 | E | + | | | 59353 208 | F | | - | 23 26 | G | = | | - | 3229 13 | | (1) |
| | | 26 5 | B | + | | | 46 5 | C | + | | | 6 5 | D | + | | | 83 20 | E | | - | 25969 40 | F | + | | | 23 5 | G | = | | | 6458 5 | | (2) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 | | | | A | | - | 10 13 | C | + | | | 10 13 | D | + | | | 21 104 | E | + | | | 59353 208 | F | | - | 23 26 | G | = | | - | 3229 13 | | (1) |
| | B | + | | | 23 13 | C | + | | | 3 13 | D | + | | | 83 104 | E | | - | 25969 208 | F | + | | | 23 26 | G | = | | | 3229 13 | | (2) |
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Therefore, the solution of the equation set is:
 | | | A = | | - | 3229 13 | + | | | 10 13 | C | - | | | 10 13 | D | - | | | 21 104 | E | - | | | 59353 208 | F | + | | | 23 26 | G |
| B = | | | 3229 13 | - | | | 23 13 | C | - | | | 3 13 | D | - | | | 83 104 | E | + | | | 25969 208 | F | - | | | 23 26 | G |
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Convert the solution of the equation set to decimals:
 | | | A = | | -248.384615 | + | | | 10 13 | C | - | | | 10 13 | D | - | | | 21 104 | E | - | | | 59353 208 | F | + | | | 23 26 | G |
| B = | | 248.384615 | - | | | 23 13 | C | - | | | 3 13 | D | - | | | 83 104 | E | + | | | 25969 208 | F | - | | | 23 26 | G |
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Where: C, D, E, F, G are arbitrary constants. 解方程组的详细方法请参阅:《多元一次方程组的解法》 |