detailed information: The input equation set is:
| | | | | 43 2 | A | | - | 35 2 | B | | - | 5 2 | C | = | | 0 | | (1) |
| - | 35 2 | A | + | | | 51 2 | B | + | | | 21 2 | C | = | | -14 | | (2) |
| - | 5 2 | A | + | | | 21 2 | B | + | | | 25 2 | C | = | | -14 | | (3) |
| | Question solving process:
Multiply both sides of equation (1) by 35 Divide the two sides of equation (1) by 43, the equation can be obtained: | | | 35 2 | A | | - | 1225 86 | B | | - | 175 86 | C | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
| | | | | 43 2 | A | | - | 35 2 | B | | - | 5 2 | C | = | | 0 | | (1) |
| | | 484 43 | B | + | | | 364 43 | C | = | | -14 | | (2) |
| - | 5 2 | A | + | | | 21 2 | B | + | | | 25 2 | C | = | | -14 | | (3) |
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Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 43, the equation can be obtained: | | | 5 2 | A | | - | 175 86 | B | | - | 25 86 | C | = | | 0 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | | | 43 2 | A | | - | 35 2 | B | | - | 5 2 | C | = | | 0 | | (1) |
| | | 484 43 | B | + | | | 364 43 | C | = | | -14 | | (2) |
| | | 364 43 | B | + | | | 525 43 | C | = | | -14 | | (3) |
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Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 43, the equation can be obtained: | | | 3 2 | A | | - | 105 86 | B | | - | 15 86 | C | = | | 0 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | 43 2 | A | | - | 35 2 | B | | - | 5 2 | C | = | | 0 | | (1) |
| | | 484 43 | B | + | | | 364 43 | C | = | | -14 | | (2) |
| | | 364 43 | B | + | | | 525 43 | C | = | | -14 | | (3) |
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Multiply both sides of equation (2) by 91 Divide the two sides of equation (2) by 121, the equation can be obtained: | | | 364 43 | B | + | | | 33124 5203 | C | = | | - | 1274 121 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | | 43 2 | A | | - | 35 2 | B | | - | 5 2 | C | = | | 0 | | (1) |
| | | 484 43 | B | + | | | 364 43 | C | = | | -14 | | (2) |
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Multiply both sides of equation (2) by 19 Divide the two sides of equation (2) by 968, the equation can be obtained: | | | 19 86 | B | + | | | 1729 10406 | C | = | | - | 133 484 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | | 43 2 | A | | - | 35 2 | B | | - | 5 2 | C | = | | 0 | | (1) |
| | | 484 43 | B | + | | | 364 43 | C | = | | -14 | | (2) |
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Divide the two sides of equation (3) by 707, the equation can be obtained: | | | 101 12221 | C | = | | - | 60 12221 | (10) | , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | | 43 2 | A | | - | 35 2 | B | | - | 5 2 | C | = | | 0 | | (1) |
| | | 484 43 | B | + | | | 364 43 | C | = | | -14 | | (2) |
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由第(4)方程式可以看出,该方程组无解。
解方程组的详细方法请参阅:《多元一次方程组的解法》 |