detailed information: The input equation set is:
| | | | | 1000 | B | + | | 510 | C | + | | 330 | D | = | | 12 | | (2) |
| | 1020 | A | | -1000 | B | | -330 | D | = | | -6 | | (3) |
| | Question solving process:
Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | | 1000 | B | + | | 510 | C | + | | 330 | D | = | | 12 | | (2) |
| -1000 | B | | -510 | C | | -330 | D | = | | -12 | | (3) |
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Add both sides of equation (2) to both sides of equation (3) ,the equations are reduced to:
| | | | | 1000 | B | + | | 510 | C | + | | 330 | D | = | | 12 | | (2) |
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Divide the two sides of equation (2) by 1000, the equation can be obtained: | | B | + | | | 51 100 | C | + | | | 33 100 | D | = | | | 3 250 | (5) | , then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
| | | | | 1000 | B | + | | 510 | C | + | | 330 | D | = | | 12 | | (2) |
| | - | 51 100 | C | | - | 133 100 | D | = | | - | 3 250 | | (4) |
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交After the exchange of equation (3) and equation (4), the equation system becomes:
| | | | | 1000 | B | + | | 510 | C | + | | 330 | D | = | | 12 | | (2) |
| - | 51 100 | C | | - | 133 100 | D | = | | - | 3 250 | | (3) |
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Multiply both sides of equation (3) by 1000, get the equation:, then add the two sides of equation (6) to both sides of equation (2), get the equation:
| | | | | - | 51 100 | C | | - | 133 100 | D | = | | - | 3 250 | | (3) |
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Multiply both sides of equation (3) by 1000, get the equation:, then add the two sides of equation (7) to both sides of equation (1), get the equation:
| | | | | - | 51 100 | C | | - | 133 100 | D | = | | - | 3 250 | | (3) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
Where: 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》 |