detailed information: The input equation set is:
| | | | 80 | x | + | | | 81 10 | y | + | | | 9 10 | z | = | | 43 | | (1) |
| | | Question solving process:
Multiply both sides of equation (1) by 81 Divide the two sides of equation (1) by 80, the equation can be obtained: | | 81 | x | + | | | 6561 800 | y | + | | | 729 800 | z | = | | | 3483 80 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | 80 | x | + | | | 81 10 | y | + | | | 9 10 | z | = | | 43 | | (1) |
| | | 639 800 | y | + | | | 71 800 | z | = | | - | 43 80 | | (2) |
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Multiply both sides of equation (1) by 9 Divide the two sides of equation (1) by 8, the equation can be obtained: | | 90 | x | + | | | 729 80 | y | + | | | 81 80 | z | = | | | 387 8 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | 80 | x | + | | | 81 10 | y | + | | | 9 10 | z | = | | 43 | | (1) |
| | | 639 800 | y | + | | | 71 800 | z | = | | - | 43 80 | | (2) |
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Multiply both sides of equation (2) by 10 Divide the two sides of equation (2) by 9, the equation can be obtained: | | | 71 80 | y | + | | | 71 720 | z | = | | - | 43 72 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | 80 | x | + | | | 81 10 | y | + | | | 9 10 | z | = | | 43 | | (1) |
| | | 639 800 | y | + | | | 71 800 | z | = | | - | 43 80 | | (2) |
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Multiply both sides of equation (3) by 639 Divide both sides of equation (3) by 800, get the equation:, then add the two sides of equation (7) to both sides of equation (2), get the equation:
| | | | 80 | x | + | | | 81 10 | y | + | | | 9 10 | z | = | | 43 | | (1) |
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Multiply both sides of equation (3) by 81 Divide both sides of equation (3) by 10, get the equation:, then add the two sides of equation (8) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 720 Divide both sides of equation (2) by 71, 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》 |