detailed information: The input equation set is:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | + | | 8 | D | = | | 21 | | (1) |
| | 4 | A | + | | 5 | B | + | | 5 | C | + | | 9 | D | = | | 42 | | (2) |
| | 3 | A | + | | 8 | B | + | | 7 | C | + | | 8 | D | = | | 56 | | (3) |
| | 2 | A | + | | 3 | B | + | | 5 | C | + | | 4 | D | = | | 17 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 4 Divide the two sides of equation (1) by 5, the equation can be obtained: | | 4 | A | + | | | 28 5 | B | + | | | 24 5 | C | + | | | 32 5 | D | = | | | 84 5 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | + | | 8 | D | = | | 21 | | (1) |
| - | 3 5 | B | + | | | 1 5 | C | + | | | 13 5 | D | = | | | 126 5 | | (2) |
| | 3 | A | + | | 8 | B | + | | 7 | C | + | | 8 | D | = | | 56 | | (3) |
| | 2 | A | + | | 3 | B | + | | 5 | C | + | | 4 | D | = | | 17 | | (4) |
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Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 5, the equation can be obtained: | | 3 | A | + | | | 21 5 | B | + | | | 18 5 | C | + | | | 24 5 | D | = | | | 63 5 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | + | | 8 | D | = | | 21 | | (1) |
| - | 3 5 | B | + | | | 1 5 | C | + | | | 13 5 | D | = | | | 126 5 | | (2) |
| | | 19 5 | B | + | | | 17 5 | C | + | | | 16 5 | D | = | | | 217 5 | | (3) |
| | 2 | A | + | | 3 | B | + | | 5 | C | + | | 4 | D | = | | 17 | | (4) |
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Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 5, the equation can be obtained: | | 2 | A | + | | | 14 5 | B | + | | | 12 5 | C | + | | | 16 5 | D | = | | | 42 5 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | + | | 8 | D | = | | 21 | | (1) |
| - | 3 5 | B | + | | | 1 5 | C | + | | | 13 5 | D | = | | | 126 5 | | (2) |
| | | 19 5 | B | + | | | 17 5 | C | + | | | 16 5 | D | = | | | 217 5 | | (3) |
| | | 1 5 | B | + | | | 13 5 | C | + | | | 4 5 | D | = | | | 43 5 | | (4) |
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Multiply both sides of equation (2) by 19 Divide the two sides of equation (2) by 3, the equation can be obtained: | - | 19 5 | B | + | | | 19 15 | C | + | | | 247 15 | D | = | | | 798 5 | (8) | , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | + | | 8 | D | = | | 21 | | (1) |
| - | 3 5 | B | + | | | 1 5 | C | + | | | 13 5 | D | = | | | 126 5 | | (2) |
| | | | 1 5 | B | + | | | 13 5 | C | + | | | 4 5 | D | = | | | 43 5 | | (4) |
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Divide the two sides of equation (2) by 3, the equation can be obtained: | - | 1 5 | B | + | | | 1 15 | C | + | | | 13 15 | D | = | | | 42 5 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | + | | 8 | D | = | | 21 | | (1) |
| - | 3 5 | B | + | | | 1 5 | C | + | | | 13 5 | D | = | | | 126 5 | | (2) |
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Multiply both sides of equation (3) by 4 Divide the two sides of equation (3) by 7, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | + | | 8 | D | = | | 21 | | (1) |
| - | 3 5 | B | + | | | 1 5 | C | + | | | 13 5 | D | = | | | 126 5 | | (2) |
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Multiply both sides of equation (4) by 413 Divide both sides of equation (4) by 201, get the equation:, then add the two sides of equation (11) to both sides of equation (3), get the equation:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | + | | 8 | D | = | | 21 | | (1) |
| - | 3 5 | B | + | | | 1 5 | C | + | | | 13 5 | D | = | | | 126 5 | | (2) |
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Multiply both sides of equation (4) by 91 Divide both sides of equation (4) by 335, get the equation:, then add the two sides of equation (12) to both sides of equation (2), get the equation:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | + | | 8 | D | = | | 21 | | (1) |
| - | 3 5 | B | + | | | 1 5 | C | = | | - | 567 335 | | (2) |
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Multiply both sides of equation (4) by 56 Divide both sides of equation (4) by 67, get the equation:, then add the two sides of equation (13) to both sides of equation (1), get the equation:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | = | | - | 4137 67 | | (1) |
| - | 3 5 | B | + | | | 1 5 | C | = | | - | 567 335 | | (2) |
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Multiply both sides of equation (3) by 3 Divide both sides of equation (3) by 70, get the equation:, then subtract both sides of equation (14) from both sides of equation (2), get the equation:
| | | | 5 | A | + | | 7 | B | + | | 6 | C | = | | - | 4137 67 | | (1) |
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Multiply both sides of equation (3) by 9 Divide both sides of equation (3) by 7, get the equation:, then subtract both sides of equation (15) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 35 Divide both sides of equation (2) by 3, get the equation:, then add the two sides of equation (16) 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》 |