detailed information: The input equation set is:
| | | | | | -2 | A | + | | D | | -12 | E | | -54 | F | = | | 0 | | (4) |
| | | Question solving process:
Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 7, the equation can be obtained: | | 2 | A | | - | 6 7 | B | | - | 8 7 | D | = | | - | 72 7 | (7) | , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
| | | | | | - | 6 7 | B | | - | 1 7 | D | | -12 | E | | -54 | F | = | | - | 72 7 | | (4) |
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Divide the two sides of equation (1) by 7, the equation can be obtained: | | A | | - | 3 7 | B | | - | 4 7 | D | = | | - | 36 7 | (8) | , then subtract both sides of equation (8) from both sides of equation (6), the equations are reduced to:
| | | | | | - | 6 7 | B | | - | 1 7 | D | | -12 | E | | -54 | F | = | | - | 72 7 | | (4) |
| | - | 4 7 | B | + | | | 4 7 | D | | -4 | F | = | | | 36 7 | | (6) |
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Multiply both sides of equation (2) by 2, the equation can be obtained: , then add the two sides of equation (9) to both sides of equation (3), the equations are reduced to:
| | | | | | - | 6 7 | B | | - | 1 7 | D | | -12 | E | | -54 | F | = | | - | 72 7 | | (4) |
| | - | 4 7 | B | + | | | 4 7 | D | | -4 | F | = | | | 36 7 | | (6) |
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Multiply both sides of equation (2) by 6 Divide the two sides of equation (2) 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:
| | | | | | - | 1 7 | D | | -12 | E | | -54 | F | = | | | 18 7 | | (4) |
| | - | 4 7 | B | + | | | 4 7 | D | | -4 | F | = | | | 36 7 | | (6) |
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Subtract both sides of equation (2) from both sides of equation (5) ,the equations are reduced to:
| | | | | | - | 1 7 | D | | -12 | E | | -54 | F | = | | | 18 7 | | (4) |
| | - | 4 7 | B | + | | | 4 7 | D | | -4 | F | = | | | 36 7 | | (6) |
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Multiply both sides of equation (2) by 4 Divide the two sides of equation (2) by 7, the equation can be obtained: , then add the two sides of equation (11) to both sides of equation (6), the equations are reduced to:
| | | | | | - | 1 7 | D | | -12 | E | | -54 | F | = | | | 18 7 | | (4) |
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Divide the two sides of equation (3) by 3, the equation can be obtained: , then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
| | | | | | - | 1 7 | D | | -12 | E | | -54 | F | = | | | 18 7 | | (4) |
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Multiply both sides of equation (4) by 4, the equation can be obtained: | - | 4 7 | D | | -48 | E | | -216 | F | = | | | 72 7 | (13) | , then add the two sides of equation (13) to both sides of equation (6), the equations are reduced to:
| | | | | | - | 1 7 | D | | -12 | E | | -54 | F | = | | | 18 7 | | (4) |
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Multiply both sides of equation (5) by 48, the equation can be obtained: , then subtract both sides of equation (14) from both sides of equation (6), the equations are reduced to:
| | | | | | - | 1 7 | D | | -12 | E | | -54 | F | = | | | 18 7 | | (4) |
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Multiply both sides of equation (6) by 27 Divide both sides of equation (6) by 110, get the equation:, then subtract both sides of equation (15) from both sides of equation (4), get the equation:
| | | | | | - | 1 7 | D | | -12 | E | = | | - | 14886 385 | | (4) |
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Multiply both sides of equation (5) by 12, get the equation:, then subtract both sides of equation (16) from both sides of equation (4), get the equation:
Multiply both sides of equation (4) by 28, get the equation:, then subtract both sides of equation (17) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 3, get the equation:, then add the two sides of equation (18) 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》 |