detailed information: The input equation set is:
 | | | | -2 | A | | -2 | B | + | | 3 | C | + | | 3 | D | = | | 0 | | (1) |
| | | 9 | A | | -11 | B | | -11 | C | + | | 9 | D | = | | 0 | | (2) |
| | | Question solving process:
Multiply both sides of equation (1) by 9 Divide the two sides of equation (1) by 2, the equation can be obtained: | | -9 | A | | -9 | B | + | | | 27 2 | C | + | | | 27 2 | D | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 | | | | -2 | A | | -2 | B | + | | 3 | C | + | | 3 | D | = | | 0 | | (1) |
| | -20 | B | + | | | 5 2 | C | + | | | 45 2 | D | = | | 0 | | (2) |
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Divide the two sides of equation (2) by 20, the equation can be obtained: , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 | | | | -2 | A | | -2 | B | + | | 3 | C | + | | 3 | D | = | | 0 | | (1) |
| | -20 | B | + | | | 5 2 | C | + | | | 45 2 | D | = | | 0 | | (2) |
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Multiply both sides of equation (3) by 20, get the equation:, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
 | | | | -2 | A | | -2 | B | + | | 3 | C | + | | 3 | D | = | | 0 | | (1) |
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Multiply both sides of equation (3) by 24, get the equation:, then subtract both sides of equation (8) from both sides of equation (1), get the equation:
Divide both sides of equation (2) by 10, get the equation:, then subtract both sides of equation (9) from both sides of equation (1), get the equation:
The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
Where: D 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》 |