detailed information: The input equation set is:
![](img/zku_y.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
| | | | | Question solving process:
Divide the two sides of equation (1) by 36, the equation can be obtained: | | A | | - | 1 3 | B | + | | | 1 6 | C | | - | 5 18 | D | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
![](img/zku.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
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Divide the two sides of equation (1) by 36, the equation can be obtained: | | A | | - | 1 3 | B | + | | | 1 6 | C | | - | 5 18 | D | = | | 0 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
![](img/zku.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
| | | | | 1 3 | B | | - | 7 6 | C | + | | | 5 18 | D | + | | E | = | | 0 | | (4) |
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Divide the two sides of equation (2) by 7, the equation can be obtained: | | | 1 3 | B | | - | 1 42 | C | + | | | 5 126 | D | = | | | 2 7 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
![](img/zku.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
| | | - | 8 7 | C | + | | | 5 21 | D | + | | E | = | | - | 2 7 | | (4) |
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Multiply both sides of equation (2) by 3 Divide the two sides of equation (2) by 7, the equation can be obtained: , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
![](img/zku.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
| | | - | 8 7 | C | + | | | 5 21 | D | + | | E | = | | - | 2 7 | | (4) |
| | | 1 14 | C | | - | 47 42 | D | | -1 | E | = | | - | 6 7 | | (5) |
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Multiply both sides of equation (3) by 8 Divide the two sides of equation (3) by 7, the equation can be obtained: , then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
![](img/zku.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
| | | | | | 1 14 | C | | - | 47 42 | D | | -1 | E | = | | - | 6 7 | | (5) |
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Divide the two sides of equation (3) by 14, the equation can be obtained: , then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
![](img/zku.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
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Multiply both sides of equation (4) by 25 Divide the two sides of equation (4) by 29, the equation can be obtained: | | | 25 21 | D | + | | | 25 29 | E | = | | | 50 29 | (12) | , then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
![](img/zku.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
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Multiply both sides of equation (5) by 29 Divide both sides of equation (5) by 4, get the equation:, then add the two sides of equation (13) to both sides of equation (4), get the equation:
![](img/zku.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
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Multiply both sides of equation (4) by 21 Divide both sides of equation (4) by 29, get the equation:, then subtract both sides of equation (14) from both sides of equation (3), get the equation:
![](img/zku.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
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Multiply both sides of equation (4) by 35 Divide both sides of equation (4) by 174, get the equation:, then subtract both sides of equation (15) from both sides of equation (2), get the equation:
![](img/zku.png) | | | | 36 | A | | -12 | B | + | | 6 | C | | -10 | D | = | | 0 | | (1) |
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Multiply both sides of equation (4) by 210 Divide both sides of equation (4) by 29, get the equation:, then add the two sides of equation (16) to both sides of equation (1), get the equation:
Divide both sides of equation (3) by 6, get the equation:, then add the two sides of equation (17) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 6, get the equation:, then subtract both sides of equation (18) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 36 Divide both sides of equation (2) by 7, get the equation:, then add the two sides of equation (19) to 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:
Convert the solution of the equation set to decimals:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |