detailed information: The input equation set is:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | + | | 3 | D | = | | 2020 | | (1) |
| | 3 | A | + | | 3 | B | + | | 3 | C | + | | 5 | D | = | | 2021 | | (2) |
| | 3 | A | + | | 5 | B | + | | 3 | C | + | | 3 | D | = | | 2023 | | (3) |
| | 3 | A | + | | 3 | B | + | | 5 | C | + | | 3 | D | = | | 2024 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 5, the equation can be obtained: | | 3 | A | + | | | 9 5 | B | + | | | 9 5 | C | + | | | 9 5 | D | = | | 1212 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | + | | 3 | D | = | | 2020 | | (1) |
| | | 6 5 | B | + | | | 6 5 | C | + | | | 16 5 | D | = | | 809 | | (2) |
| | 3 | A | + | | 5 | B | + | | 3 | C | + | | 3 | D | = | | 2023 | | (3) |
| | 3 | A | + | | 3 | B | + | | 5 | C | + | | 3 | D | = | | 2024 | | (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 | + | | | 9 5 | B | + | | | 9 5 | C | + | | | 9 5 | D | = | | 1212 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | + | | 3 | D | = | | 2020 | | (1) |
| | | 6 5 | B | + | | | 6 5 | C | + | | | 16 5 | D | = | | 809 | | (2) |
| | | 16 5 | B | + | | | 6 5 | C | + | | | 6 5 | D | = | | 811 | | (3) |
| | 3 | A | + | | 3 | B | + | | 5 | C | + | | 3 | D | = | | 2024 | | (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 | + | | | 9 5 | B | + | | | 9 5 | C | + | | | 9 5 | D | = | | 1212 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | + | | 3 | D | = | | 2020 | | (1) |
| | | 6 5 | B | + | | | 6 5 | C | + | | | 16 5 | D | = | | 809 | | (2) |
| | | 16 5 | B | + | | | 6 5 | C | + | | | 6 5 | D | = | | 811 | | (3) |
| | | 6 5 | B | + | | | 16 5 | C | + | | | 6 5 | D | = | | 812 | | (4) |
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Multiply both sides of equation (2) by 8 Divide the two sides of equation (2) by 3, the equation can be obtained: | | | 16 5 | B | + | | | 16 5 | C | + | | | 128 15 | D | = | | | 6472 3 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | + | | 3 | D | = | | 2020 | | (1) |
| | | 6 5 | B | + | | | 6 5 | C | + | | | 16 5 | D | = | | 809 | | (2) |
| | | | 6 5 | B | + | | | 16 5 | C | + | | | 6 5 | D | = | | 812 | | (4) |
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Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | + | | 3 | D | = | | 2020 | | (1) |
| | | 6 5 | B | + | | | 6 5 | C | + | | | 16 5 | D | = | | 809 | | (2) |
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Add both sides of equation (3) to both sides of equation (4) ,the equations are reduced to:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | + | | 3 | D | = | | 2020 | | (1) |
| | | 6 5 | B | + | | | 6 5 | C | + | | | 16 5 | D | = | | 809 | | (2) |
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Multiply both sides of equation (4) by 11 Divide both sides of equation (4) by 14, get the equation:, then subtract both sides of equation (9) from both sides of equation (3), get the equation:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | + | | 3 | D | = | | 2020 | | (1) |
| | | 6 5 | B | + | | | 6 5 | C | + | | | 16 5 | D | = | | 809 | | (2) |
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Multiply both sides of equation (4) by 12 Divide both sides of equation (4) by 35, get the equation:, then add the two sides of equation (10) to both sides of equation (2), get the equation:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | + | | 3 | D | = | | 2020 | | (1) |
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Multiply both sides of equation (4) by 9 Divide both sides of equation (4) by 28, get the equation:, then add the two sides of equation (11) to both sides of equation (1), get the equation:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | = | | | 22235 14 | | (1) |
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Multiply both sides of equation (3) by 3 Divide both sides of equation (3) by 5, get the equation:, then add the two sides of equation (12) to both sides of equation (2), get the equation:
| | | | 5 | A | + | | 3 | B | + | | 3 | C | = | | | 22235 14 | | (1) |
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Multiply both sides of equation (3) by 3 Divide both sides of equation (3) by 2, 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 2, 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》 |