detailed information: The input equation set is:
| | | | -8 | A | | -4 | B | + | | 8 | C | + | | 16 | D | = | | 360 | | (2) |
| -12 | A | | -8 | B | + | | 4 | C | + | | 12 | D | = | | -440 | | (3) |
| -20 | A | | -16 | B | | -4 | C | + | | 4 | D | = | | -1680 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 8, the equation can be obtained: | | 8 | A | + | | 8 | B | + | | 8 | C | + | | 8 | D | = | | -1280 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
| | | | | 4 | B | + | | 16 | C | + | | 24 | D | = | | -920 | | (2) |
| -12 | A | | -8 | B | + | | 4 | C | + | | 12 | D | = | | -440 | | (3) |
| -20 | A | | -16 | B | | -4 | C | + | | 4 | D | = | | -1680 | | (4) |
|
Multiply both sides of equation (1) by 12, the equation can be obtained: | | 12 | A | + | | 12 | B | + | | 12 | C | + | | 12 | D | = | | -1920 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | | | 4 | B | + | | 16 | C | + | | 24 | D | = | | -920 | | (2) |
| | 4 | B | + | | 16 | C | + | | 24 | D | = | | -2360 | | (3) |
| -20 | A | | -16 | B | | -4 | C | + | | 4 | D | = | | -1680 | | (4) |
|
Multiply both sides of equation (1) by 20, the equation can be obtained: | | 20 | A | + | | 20 | B | + | | 20 | C | + | | 20 | D | = | | -3200 | (7) | , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
| | | | | 4 | B | + | | 16 | C | + | | 24 | D | = | | -920 | | (2) |
| | 4 | B | + | | 16 | C | + | | 24 | D | = | | -2360 | | (3) |
| | 4 | B | + | | 16 | C | + | | 24 | D | = | | -4880 | | (4) |
|
Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
| | | | | 4 | B | + | | 16 | C | + | | 24 | D | = | | -920 | | (2) |
| | | 4 | B | + | | 16 | C | + | | 24 | D | = | | -4880 | | (4) |
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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》 |