detailed information: The input equation set is:
 | | | | | 16 25 | A | | - | 2 5 | B | | - | 2 5 | C | + | | | 1 5 | D | = | | -1 | | (1) |
| - | 1 5 | A | + | | | 1 5 | B | + | | | 1 5 | C | | - | 1 5 | D | = | | 0 | | (2) |
| - | 1 5 | A | + | | | 1 5 | B | + | | | 1 5 | C | | - | 1 5 | D | = | | 0 | | (3) |
| | | 1 5 | A | | - | 1 5 | B | | - | 1 5 | C | + | | | 1 5 | D | = | | -1 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 16, the equation can be obtained: | | | 1 5 | A | | - | 1 8 | B | | - | 1 8 | C | + | | | 1 16 | D | = | | - | 5 16 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 | | | | | 16 25 | A | | - | 2 5 | B | | - | 2 5 | C | + | | | 1 5 | D | = | | -1 | | (1) |
| | | 3 40 | B | + | | | 3 40 | C | | - | 11 80 | D | = | | - | 5 16 | | (2) |
| - | 1 5 | A | + | | | 1 5 | B | + | | | 1 5 | C | | - | 1 5 | D | = | | 0 | | (3) |
| | | 1 5 | A | | - | 1 5 | B | | - | 1 5 | C | + | | | 1 5 | D | = | | -1 | | (4) |
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Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 16, the equation can be obtained: | | | 1 5 | A | | - | 1 8 | B | | - | 1 8 | C | + | | | 1 16 | D | = | | - | 5 16 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 | | | | | 16 25 | A | | - | 2 5 | B | | - | 2 5 | C | + | | | 1 5 | D | = | | -1 | | (1) |
| | | 3 40 | B | + | | | 3 40 | C | | - | 11 80 | D | = | | - | 5 16 | | (2) |
| | | 3 40 | B | + | | | 3 40 | C | | - | 11 80 | D | = | | - | 5 16 | | (3) |
| | | 1 5 | A | | - | 1 5 | B | | - | 1 5 | C | + | | | 1 5 | D | = | | -1 | | (4) |
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Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 16, the equation can be obtained: | | | 1 5 | A | | - | 1 8 | B | | - | 1 8 | C | + | | | 1 16 | D | = | | - | 5 16 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 | | | | | 16 25 | A | | - | 2 5 | B | | - | 2 5 | C | + | | | 1 5 | D | = | | -1 | | (1) |
| | | 3 40 | B | + | | | 3 40 | C | | - | 11 80 | D | = | | - | 5 16 | | (2) |
| | | 3 40 | B | + | | | 3 40 | C | | - | 11 80 | D | = | | - | 5 16 | | (3) |
| - | 3 40 | B | | - | 3 40 | C | + | | | 11 80 | D | = | | - | 11 16 | | (4) |
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Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
 | | | | | 16 25 | A | | - | 2 5 | B | | - | 2 5 | C | + | | | 1 5 | D | = | | -1 | | (1) |
| | | 3 40 | B | + | | | 3 40 | C | | - | 11 80 | D | = | | - | 5 16 | | (2) |
| | - | 3 40 | B | | - | 3 40 | C | + | | | 11 80 | D | = | | - | 11 16 | | (4) |
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Add both sides of equation (2) to both sides of equation (4) ,the equations are reduced to:
 | | | | | 16 25 | A | | - | 2 5 | B | | - | 2 5 | C | + | | | 1 5 | D | = | | -1 | | (1) |
| | | 3 40 | B | + | | | 3 40 | C | | - | 11 80 | D | = | | - | 5 16 | | (2) |
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由第(4)方程式可以看出,该方程组无解。
解方程组的详细方法请参阅:《多元一次方程组的解法》 |