detailed information: The input equation set is: Question solving process:
Multiply both sides of equation (1) by 320 Divide the two sides of equation (1) by 203, the equation can be obtained: | | 320 | x | + | | | 12480 203 | y | + | | | 320 29 | z | = | | | 320 203 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | - | 1924 203 | y | | - | 88 29 | z | = | | - | 117 203 | | (2) |
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Multiply both sides of equation (1) by 671 Divide the two sides of equation (1) by 203, the equation can be obtained: | | 671 | x | + | | | 26169 203 | y | + | | | 671 29 | z | = | | | 671 203 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | - | 1924 203 | y | | - | 88 29 | z | = | | - | 117 203 | | (2) |
| - | 7696 203 | y | | - | 352 29 | z | = | | - | 468 203 | | (3) |
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Multiply both sides of equation (2) by 4, the equation can be obtained: | - | 7696 203 | y | | - | 352 29 | z | = | | - | 468 203 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | - | 1924 203 | y | | - | 88 29 | z | = | | - | 117 203 | | (2) |
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Multiply both sides of equation (2) by 609 Divide both sides of equation (2) by 148, get the equation: | -39 | y | | - | 462 37 | z | = | | - | 351 148 | (7) | , then add the two sides of equation (7) to both sides of equation (1), get the equation:
| | | | 203 | x | | - | 203 37 | z | = | | - | 203 148 | | (1) |
| - | 1924 203 | y | | - | 88 29 | z | = | | - | 117 203 | | (2) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
| | | | | y | + | | | 154 481 | z | = | | | 117 1924 | | (2) |
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Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
Where: z 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》 |