detailed information: The input equation set is:
| | | | | 546 | x | + | | 180 | y | + | | 537 | z | = | | 1 | | (2) |
| | 154 | x | + | | 50 | y | + | | 149 | z | = | | 0 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 546 Divide the two sides of equation (1) by 25, the equation can be obtained: | -546 | x | | - | 4914 25 | y | | - | 14742 25 | z | = | | 0 | (4) | , then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
| | | | - | 414 25 | y | | - | 1317 25 | z | = | | 1 | | (2) |
| | 154 | x | + | | 50 | y | + | | 149 | z | = | | 0 | | (3) |
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Multiply both sides of equation (1) by 154 Divide the two sides of equation (1) by 25, the equation can be obtained: | -154 | x | | - | 1386 25 | y | | - | 4158 25 | z | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
| | | | - | 414 25 | y | | - | 1317 25 | z | = | | 1 | | (2) |
| - | 136 25 | y | | - | 433 25 | z | = | | 0 | | (3) |
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Multiply both sides of equation (2) by 68 Divide the two sides of equation (2) by 207, the equation can be obtained: | - | 136 25 | y | | - | 29852 1725 | z | = | | | 68 207 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | - | 414 25 | y | | - | 1317 25 | z | = | | 1 | | (2) |
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Multiply both sides of equation (3) by 90873 Divide both sides of equation (3) by 25, get the equation: | - | 1317 25 | z | = | | - | 29852 25 | (7) | , then subtract both sides of equation (7) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 1863, get the equation:, then subtract both sides of equation (8) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 25 Divide both sides of equation (2) by 46, get the equation:, then subtract both sides of equation (9) from both sides of equation (1), get the equation:
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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |