detailed information: The input equation set is:
| | | | | 47 5 | A | + | | | 221 5 | B | + | | | 107 2 | C | + | | | 23 2 | D | = | | | 87 5 | | (1) |
| | | 2 5 | A | + | | | 12 5 | B | + | | | 17 5 | C | + | | | 2 5 | D | = | | | 7 5 | | (2) |
| | | Question solving process:
Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 47, the equation can be obtained: | | | 2 5 | A | + | | | 442 235 | B | + | | | 107 47 | C | + | | | 23 47 | D | = | | | 174 235 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | 47 5 | A | + | | | 221 5 | B | + | | | 107 2 | C | + | | | 23 2 | D | = | | | 87 5 | | (1) |
| | | 122 235 | B | + | | | 264 235 | C | | - | 21 235 | D | = | | | 31 47 | | (2) |
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Multiply both sides of equation (2) by 10387 Divide both sides of equation (2) by 122, get the equation: | | | 10387 235 | B | + | | | 29172 305 | C | | - | 4641 610 | D | = | | | 6851 122 | (6) | , then subtract both sides of equation (6) from both sides of equation (1), get the equation:
| | | | | 47 5 | A | | - | 25709 610 | C | + | | | 5828 305 | D | = | | - | 23641 610 | | (1) |
| | | 122 235 | B | + | | | 264 235 | C | | - | 21 235 | D | = | | | 31 47 | | (2) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
| | | | A | | - | 547 122 | C | + | | | 124 61 | D | = | | - | 503 122 | | (1) |
| | B | + | | | 132 61 | C | | - | 21 122 | D | = | | | 155 122 | | (2) |
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Therefore, the solution of the equation set is:
| | | A = | | - | 503 122 | + | | | 547 122 | C | - | | | 124 61 | D |
| B = | | | 155 122 | - | | | 132 61 | C | + | | | 21 122 | D |
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Convert the solution of the equation set to decimals:
| | | A = | | -4.122951 | + | | | 547 122 | C | - | | | 124 61 | D |
| B = | | 1.270492 | - | | | 132 61 | C | + | | | 21 122 | D |
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Where: C, D are arbitrary constants. 解方程组的详细方法请参阅:《多元一次方程组的解法》 |