detailed information: The input equation set is:
| | | | -10 | A | + | | 10 | B | + | | 4 | C | = | | -20 | | (2) |
| | | | Question solving process:
Multiply both sides of equation (1) by 5, the equation can be obtained: | | 10 | A | + | | 60 | B | + | | 40 | D | = | | 200 | (6) | , then add the two sides of equation (6) to both sides of equation (2), the equations are reduced to:
Divide the two sides of equation (1) by 2, the equation can be obtained: , then add the two sides of equation (7) to both sides of equation (5), the equations are reduced to:
Divide the two sides of equation (2) by 70, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | | | - | 37 35 | C | | - | 11 7 | D | = | | - | 18 7 | | (4) |
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Divide the two sides of equation (2) by 14, the equation can be obtained: | | 5 | B | + | | | 2 7 | C | + | | | 20 7 | D | = | | | 90 7 | (9) | , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
| | | | | | - | 37 35 | C | | - | 11 7 | D | = | | - | 18 7 | | (4) |
| - | 2 7 | C | + | | | 15 7 | D | | -1 | E | = | | | 50 7 | | (5) |
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Multiply both sides of equation (3) by 37 Divide the two sides of equation (3) by 140, the equation can be obtained: | - | 37 35 | C | + | | | 74 35 | D | + | | | 74 35 | E | = | | | 37 7 | (10) | , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | | | - | 129 35 | D | | - | 74 35 | E | = | | - | 55 7 | | (4) |
| - | 2 7 | C | + | | | 15 7 | D | | -1 | E | = | | | 50 7 | | (5) |
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Divide the two sides of equation (3) by 14, the equation can be obtained: | - | 2 7 | C | + | | | 4 7 | D | + | | | 4 7 | E | = | | | 10 7 | (11) | , then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
| | | | | | - | 129 35 | D | | - | 74 35 | E | = | | - | 55 7 | | (4) |
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Multiply both sides of equation (4) by 55 Divide the two sides of equation (4) by 129, the equation can be obtained: | - | 11 7 | D | | - | 814 903 | E | = | | - | 3025 903 | (12) | , then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
| | | | | | - | 129 35 | D | | - | 74 35 | E | = | | - | 55 7 | | (4) |
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Multiply both sides of equation (5) by 9546 Divide both sides of equation (5) by 11165, get the equation:, then subtract both sides of equation (13) from both sides of equation (4), get the equation:
| | | | | | - | 129 35 | D | = | | - | 22059 2233 | | (4) |
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Multiply both sides of equation (5) by 1032 Divide both sides of equation (5) by 319, get the equation:, then add the two sides of equation (14) to both sides of equation (3), get the equation:
| | | | | | - | 129 35 | D | = | | - | 22059 2233 | | (4) |
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Multiply both sides of equation (4) by 280 Divide both sides of equation (4) by 129, get the equation:, then add the two sides of equation (15) to both sides of equation (3), get the equation:
| | | | | | - | 129 35 | D | = | | - | 22059 2233 | | (4) |
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Multiply both sides of equation (4) by 1400 Divide both sides of equation (4) by 129, get the equation:, then add the two sides of equation (16) to both sides of equation (2), get the equation:
| | | | | | - | 129 35 | D | = | | - | 22059 2233 | | (4) |
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Multiply both sides of equation (4) by 280 Divide both sides of equation (4) by 129, get the equation:, then add the two sides of equation (17) to both sides of equation (1), get the equation:
| | | | | | - | 129 35 | D | = | | - | 22059 2233 | | (4) |
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Add both sides of equation (3) to both sides of equation (2), get the equation:
Multiply both sides of equation (2) by 6 Divide both sides of equation (2) by 35, get the equation:, then subtract both sides of equation (18) 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》 |