detailed information: The input equation set is: Question solving process:
Multiply both sides of equation (1) by 10, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (2) by 20, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | | | | 24 | C | + | | 20 | D | + | | 10 | F | = | | -20 | | (4) |
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Multiply both sides of equation (2) by 10, the equation can be obtained: , then subtract both sides of equation (9) from both sides of equation (6), the equations are reduced to:
| | | | | | | 24 | C | + | | 20 | D | + | | 10 | F | = | | -20 | | (4) |
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交After the exchange of equation (3) and equation (4), the equation system becomes:
| | | | | | 24 | C | + | | 20 | D | + | | 10 | F | = | | -20 | | (3) |
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Divide the two sides of equation (3) by 6, the equation can be obtained: | | 4 | C | + | | | 10 3 | D | + | | | 5 3 | F | = | | - | 10 3 | (10) | , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
| | | | | | 24 | C | + | | 20 | D | + | | 10 | F | = | | -20 | | (3) |
| | - | 34 3 | D | | -8 | E | | - | 5 3 | F | = | | - | 50 3 | | (5) |
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Multiply both sides of equation (3) by 5 Divide the two sides of equation (3) by 12, the equation can be obtained: | | 10 | C | + | | | 25 3 | D | + | | | 25 6 | F | = | | - | 25 3 | (11) | , then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
| | | | | | 24 | C | + | | 20 | D | + | | 10 | F | = | | -20 | | (3) |
| | - | 34 3 | D | | -8 | E | | - | 5 3 | F | = | | - | 50 3 | | (5) |
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Multiply both sides of equation (4) by 34 Divide the two sides of equation (4) by 3, the equation can be obtained: | | | 34 3 | D | | - | 34 3 | E | + | | | 34 3 | F | = | | 0 | (12) | , then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
| | | | | | 24 | C | + | | 20 | D | + | | 10 | F | = | | -20 | | (3) |
| | - | 58 3 | E | + | | | 29 3 | F | = | | - | 50 3 | | (5) |
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Multiply both sides of equation (4) by 29 Divide the two sides of equation (4) by 3, the equation can be obtained: | | | 29 3 | D | | - | 29 3 | E | + | | | 29 3 | F | = | | 0 | (13) | , then subtract both sides of equation (13) from both sides of equation (6), the equations are reduced to:
| | | | | | 24 | C | + | | 20 | D | + | | 10 | F | = | | -20 | | (3) |
| | - | 58 3 | E | + | | | 29 3 | F | = | | - | 50 3 | | (5) |
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Divide the two sides of equation (5) by 2, the equation can be obtained: | - | 29 3 | E | + | | | 29 6 | F | = | | - | 25 3 | (14) | , then add the two sides of equation (14) to both sides of equation (6), the equations are reduced to:
| | | | | | 24 | C | + | | 20 | D | + | | 10 | F | = | | -20 | | (3) |
| | - | 58 3 | E | + | | | 29 3 | F | = | | - | 50 3 | | (5) |
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Multiply both sides of equation (6) by 29 Divide both sides of equation (6) by 33, get the equation:, then add the two sides of equation (15) to both sides of equation (5), get the equation:
| | | | | | 24 | C | + | | 20 | D | + | | 10 | F | = | | -20 | | (3) |
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Divide both sides of equation (6) by 11, get the equation:, then add the two sides of equation (16) to both sides of equation (4), get the equation:
| | | | | | 24 | C | + | | 20 | D | + | | 10 | F | = | | -20 | | (3) |
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Multiply both sides of equation (6) by 10 Divide both sides of equation (6) by 11, get the equation:, then add the two sides of equation (17) to both sides of equation (3), get the equation:
Divide both sides of equation (6) by 11, get the equation:, then subtract both sides of equation (18) from both sides of equation (1), get the equation:
Multiply both sides of equation (5) by 3 Divide both sides of equation (5) by 58, get the equation:, then subtract both sides of equation (19) from both sides of equation (4), get the equation:
Multiply both sides of equation (4) by 20, get the equation:, then subtract both sides of equation (20) from both sides of equation (3), get the equation:
Add both sides of equation (4) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 24, get the equation:, then add the two sides of equation (21) to both sides of equation (2), get the equation:
Add both sides of equation (2) 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》 |