detailed information: The input equation set is:
| | | | | | 36 125 | x | | - | 21 25 | y | + | | | 21 25 | z | = | | 0 | | (2) |
| | | 46 25 | x | + | | | 21 25 | y | | - | 21 25 | z | = | | 0 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 36 Divide the two sides of equation (1) by 125, the equation can be obtained: | | | 36 125 | x | + | | | 36 125 | y | + | | | 36 125 | z | = | | | 36 125 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | - | 141 125 | y | + | | | 69 125 | z | = | | - | 36 125 | | (2) |
| | | 46 25 | x | + | | | 21 25 | y | | - | 21 25 | z | = | | 0 | | (3) |
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Multiply both sides of equation (1) by 46 Divide the two sides of equation (1) by 25, the equation can be obtained: | | | 46 25 | x | + | | | 46 25 | y | + | | | 46 25 | z | = | | | 46 25 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | - | 141 125 | y | + | | | 69 125 | z | = | | - | 36 125 | | (2) |
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Multiply both sides of equation (2) by 125 Divide the two sides of equation (2) by 141, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | - | 141 125 | y | + | | | 69 125 | z | = | | - | 36 125 | | (2) |
| - | 3724 1175 | z | = | | - | 1862 1175 | | (3) |
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Multiply both sides of equation (3) by 3243 Divide both sides of equation (3) by 18620, get the equation:, then add the two sides of equation (7) to both sides of equation (2), get the equation:
| | | | | - | 3724 1175 | z | = | | - | 1862 1175 | | (3) |
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Multiply both sides of equation (3) by 1175 Divide both sides of equation (3) by 3724, get the equation:, then add the two sides of equation (8) to both sides of equation (1), get the equation:
| | | | | - | 3724 1175 | z | = | | - | 1862 1175 | | (3) |
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Multiply both sides of equation (2) by 125 Divide both sides of equation (2) by 141, get the equation:, then add the two sides of equation (9) to 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》 |