detailed information: The input equation set is:
![](img/zku_y.png) | | | | - | 3 20 | x | + | | | 1 10 | y | | - | 1 10 | z | = | | 0 | | (2) |
| - | 1 10 | x | | - | 1 10 | y | + | | | 1 10 | z | = | | 0 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 4, the equation can be obtained: | | | 3 20 | x | | - | 3 16 | y | | - | 9 80 | z | = | | 0 | (4) | , then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
![](img/zku.png) | | | | | - | 1 10 | x | | - | 1 10 | y | + | | | 1 10 | z | = | | 0 | | (3) |
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Divide the two sides of equation (1) by 2, the equation can be obtained: | | | 1 10 | x | | - | 1 8 | y | | - | 3 40 | z | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 18 Divide the two sides of equation (2) by 7, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (3) by 119 Divide both sides of equation (3) by 320, get the equation:, then add the two sides of equation (7) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 21 Divide both sides of equation (3) by 80, get the equation:, then add the two sides of equation (8) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 20 Divide both sides of equation (2) by 7, 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |