detailed information: The input equation set is:
 | | | | -2 | A | + | | 6 | B | | -3 | C | | -1 | D | = | | -4 | | (2) |
| | | Question solving process:
Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 5, the equation can be obtained: , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 | | | | | | 34 5 | B | | - | 17 5 | C | | -1 | D | = | | - | 16 5 | | (2) |
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Divide the two sides of equation (1) by 5, the equation can be obtained: , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 | | | | | | 34 5 | B | | - | 17 5 | C | | -1 | D | = | | - | 16 5 | | (2) |
| - | 13 5 | B | + | | | 19 5 | C | + | | D | = | | | 32 5 | | (3) |
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Multiply both sides of equation (2) by 13 Divide the two sides of equation (2) by 34, the equation can be obtained: | | | 13 5 | B | | - | 13 10 | C | | - | 13 34 | D | = | | - | 104 85 | (7) | , then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
 | | | | | | 34 5 | B | | - | 17 5 | C | | -1 | D | = | | - | 16 5 | | (2) |
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Multiply both sides of equation (2) by 5 Divide the two sides of equation (2) by 34, the equation can be obtained: | | B | | - | 1 2 | C | | - | 5 34 | D | = | | - | 8 17 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 | | | | | | 34 5 | B | | - | 17 5 | C | | -1 | D | = | | - | 16 5 | | (2) |
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Divide the two sides of equation (3) by 5, the equation can be obtained: , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 | | | | | | 34 5 | B | | - | 17 5 | C | | -1 | D | = | | - | 16 5 | | (2) |
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Multiply both sides of equation (4) by 105 Divide both sides of equation (4) by 46, get the equation:, then subtract both sides of equation (10) from both sides of equation (3), get the equation:
 | | | | | | 34 5 | B | | - | 17 5 | C | | -1 | D | = | | - | 16 5 | | (2) |
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Multiply both sides of equation (4) by 85 Divide both sides of equation (4) by 23, get the equation:, then add the two sides of equation (11) to both sides of equation (2), get the equation:
 | | | | | | 34 5 | B | | - | 17 5 | C | = | | | 1972 115 | | (2) |
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Multiply both sides of equation (3) by 34 Divide both sides of equation (3) by 25, get the equation:, then add the two sides of equation (12) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 5, get the equation:, then add the two sides of equation (13) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 5 Divide both sides of equation (2) by 17, get the equation:, then subtract both sides of equation (14) 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:
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》 |