detailed information: The input equation set is:
| | | | | 2594 | A | + | | 994 | B | | -606 | C | | -2206 | D | = | | 0 | | (2) |
| | 1600 | B | + | | 3200 | C | + | | 4800 | D | = | | 236054 | | (3) |
| | 1600 | A | | -1600 | C | | -3200 | D | = | | -90454 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 2594, the equation can be obtained: | | 2594 | A | + | | 2594 | B | + | | 2594 | C | + | | 2594 | D | = | | 236054 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | -1600 | B | | -3200 | C | | -4800 | D | = | | -236054 | | (2) |
| | 1600 | B | + | | 3200 | C | + | | 4800 | D | = | | 236054 | | (3) |
| | 1600 | A | | -1600 | C | | -3200 | D | = | | -90454 | | (4) |
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Multiply both sides of equation (1) by 1600, the equation can be obtained: | | 1600 | A | + | | 1600 | B | + | | 1600 | C | + | | 1600 | D | = | | 145600 | (6) | , then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
| | | | -1600 | B | | -3200 | C | | -4800 | D | = | | -236054 | | (2) |
| | 1600 | B | + | | 3200 | C | + | | 4800 | D | = | | 236054 | | (3) |
| -1600 | B | | -3200 | C | | -4800 | D | = | | -236054 | | (4) |
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Add both sides of equation (2) to both sides of equation (3) ,the equations are reduced to:
| | | | -1600 | B | | -3200 | C | | -4800 | D | = | | -236054 | | (2) |
| | -1600 | B | | -3200 | C | | -4800 | D | = | | -236054 | | (4) |
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Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
| | | | -1600 | B | | -3200 | C | | -4800 | D | = | | -236054 | | (2) |
| | |
Divide both sides of equation (2) by 1600, get the equation: | -1 | B | | -2 | C | | -3 | D | = | | - | 118027 800 | (7) | , then add the two sides of equation (7) to both sides of equation (1), get the equation:
| | | | A | | -1 | C | | -2 | D | = | | - | 45227 800 | | (1) |
| -1600 | B | | -3200 | C | | -4800 | D | = | | -236054 | | (2) |
| | |
The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
| | | | A | | -1 | C | | -2 | D | = | | - | 45227 800 | | (1) |
| | B | + | | 2 | C | + | | 3 | D | = | | | 118027 800 | | (2) |
| | |
Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
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》 |