detailed information: The input equation set is:
 | | | | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (1) |
| | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (2) |
| | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (3) |
| | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (4) |
| | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (5) |
| Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 | | | | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (1) |
| | | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (3) |
| | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (4) |
| | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 | | | | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (1) |
| | | | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (4) |
| | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (5) |
|
Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
 | | | | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (1) |
| | | | | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
 | | | | | 311 2500 | A | + | | | 311 2500 | B | + | | | 311 2500 | C | + | | | 311 2500 | D | + | | | 311 2500 | E | = | | 0 | | (1) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 | | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| | | | |
Therefore, the solution of the equation set is:
 | | | A = | - | | 311 311 | B | - | | | 311 311 | C | - | | | 311 311 | D | - | | | 311 311 | E |
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Where: B, C, D, E 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》 |