detailed information: The input equation set is:
| | | | 711 | A | + | | 5325 | B | + | | C | = | | 3030 | | (1) |
| | 744 | A | + | | 5325 | B | + | | C | = | | 3092 | | (2) |
| | 790 | A | + | | 5325 | B | + | | C | = | | 3178 | | (3) |
| | 832 | A | + | | 5325 | B | + | | C | = | | 3257 | | (4) |
| | 790 | A | + | | 5734 | B | + | | C | = | | 3317 | | (5) |
| | 832 | A | + | | 5734 | B | + | | C | = | | 3396 | | (6) |
| Question solving process:
Multiply both sides of equation (1) by 248 Divide the two sides of equation (1) by 237, the equation can be obtained: | | 744 | A | + | | | 440200 79 | B | + | | | 248 237 | C | = | | | 250480 79 | (7) | , then subtract both sides of equation (7) from both sides of equation (2), the equations are reduced to:
| | | | 711 | A | + | | 5325 | B | + | | C | = | | 3030 | | (1) |
| - | 19525 79 | B | | - | 11 237 | C | = | | - | 6212 79 | | (2) |
| | 790 | A | + | | 5325 | B | + | | C | = | | 3178 | | (3) |
| | 832 | A | + | | 5325 | B | + | | C | = | | 3257 | | (4) |
| | 790 | A | + | | 5734 | B | + | | C | = | | 3317 | | (5) |
| | 832 | A | + | | 5734 | B | + | | C | = | | 3396 | | (6) |
|
Multiply both sides of equation (1) by 790 Divide the two sides of equation (1) by 711, the equation can be obtained: | | 790 | A | + | | | 1402250 237 | B | + | | | 790 711 | C | = | | | 797900 237 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | 711 | A | + | | 5325 | B | + | | C | = | | 3030 | | (1) |
| - | 19525 79 | B | | - | 11 237 | C | = | | - | 6212 79 | | (2) |
| - | 140225 237 | B | | - | 1 9 | C | = | | - | 44714 237 | | (3) |
| | 832 | A | + | | 5325 | B | + | | C | = | | 3257 | | (4) |
| | 790 | A | + | | 5734 | B | + | | C | = | | 3317 | | (5) |
| | 832 | A | + | | 5734 | B | + | | C | = | | 3396 | | (6) |
|
Multiply both sides of equation (1) by 832 Divide the two sides of equation (1) by 711, the equation can be obtained: | | 832 | A | + | | | 1476800 237 | B | + | | | 832 711 | C | = | | | 840320 237 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | 711 | A | + | | 5325 | B | + | | C | = | | 3030 | | (1) |
| - | 19525 79 | B | | - | 11 237 | C | = | | - | 6212 79 | | (2) |
| - | 140225 237 | B | | - | 1 9 | C | = | | - | 44714 237 | | (3) |
| - | 214775 237 | B | | - | 121 711 | C | = | | - | 68411 237 | | (4) |
| | 790 | A | + | | 5734 | B | + | | C | = | | 3317 | | (5) |
| | 832 | A | + | | 5734 | B | + | | C | = | | 3396 | | (6) |
|
Multiply both sides of equation (1) by 790 Divide the two sides of equation (1) by 711, the equation can be obtained: | | 790 | A | + | | | 1402250 237 | B | + | | | 790 711 | C | = | | | 797900 237 | (10) | , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
| | | | 711 | A | + | | 5325 | B | + | | C | = | | 3030 | | (1) |
| - | 19525 79 | B | | - | 11 237 | C | = | | - | 6212 79 | | (2) |
| - | 140225 237 | B | | - | 1 9 | C | = | | - | 44714 237 | | (3) |
| - | 214775 237 | B | | - | 121 711 | C | = | | - | 68411 237 | | (4) |
| - | 43292 237 | B | | - | 1 9 | C | = | | - | 11771 237 | | (5) |
| | 832 | A | + | | 5734 | B | + | | C | = | | 3396 | | (6) |
|
Multiply both sides of equation (1) by 832 Divide the two sides of equation (1) by 711, the equation can be obtained: | | 832 | A | + | | | 1476800 237 | B | + | | | 832 711 | C | = | | | 840320 237 | (11) | , then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
| | | | 711 | A | + | | 5325 | B | + | | C | = | | 3030 | | (1) |
| - | 19525 79 | B | | - | 11 237 | C | = | | - | 6212 79 | | (2) |
| - | 140225 237 | B | | - | 1 9 | C | = | | - | 44714 237 | | (3) |
| - | 214775 237 | B | | - | 121 711 | C | = | | - | 68411 237 | | (4) |
| - | 43292 237 | B | | - | 1 9 | C | = | | - | 11771 237 | | (5) |
| - | 117842 237 | B | | - | 121 711 | C | = | | - | 35468 237 | | (6) |
|
Multiply both sides of equation (2) by 5609 Divide the two sides of equation (2) by 2343, the equation can be obtained: | - | 126025 213 | B | | - | 1 9 | C | = | | - | 441052 2343 | (12) | , then subtract both sides of equation (12) from both sides of equation (3), the equations are reduced to:
| | | | 711 | A | + | | 5325 | B | + | | C | = | | 3030 | | (1) |
| - | 19525 79 | B | | - | 11 237 | C | = | | - | 6212 79 | | (2) |
| | - | 214775 237 | B | | - | 121 711 | C | = | | - | 68411 237 | | (4) |
| - | 43292 237 | B | | - | 1 9 | C | = | | - | 11771 237 | | (5) |
| - | 117842 237 | B | | - | 121 711 | C | = | | - | 35468 237 | | (6) |
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由第(3)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》 |