detailed information: The input equation set is:
| | | | 180 | x | + | | 80 | y | + | | 340 | z | = | | 20 | | (1) |
| | 130 | x | + | | 60 | y | + | | 230 | z | = | | 22 | | (2) |
| | 380 | x | + | | 120 | y | + | | 670 | z | = | | 70 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 13 Divide the two sides of equation (1) by 18, the equation can be obtained: | | 130 | x | + | | | 520 9 | y | + | | | 2210 9 | z | = | | | 130 9 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | 180 | x | + | | 80 | y | + | | 340 | z | = | | 20 | | (1) |
| | | 380 | x | + | | 120 | y | + | | 670 | z | = | | 70 | | (3) |
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Multiply both sides of equation (1) by 19 Divide the two sides of equation (1) by 9, the equation can be obtained: | | 380 | x | + | | | 1520 9 | y | + | | | 6460 9 | z | = | | | 380 9 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | 180 | x | + | | 80 | y | + | | 340 | z | = | | 20 | | (1) |
| | - | 440 9 | y | | - | 430 9 | z | = | | | 250 9 | | (3) |
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Multiply both sides of equation (2) by 22, the equation can be obtained: | | | 440 9 | y | | - | 3080 9 | z | = | | | 1496 9 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | | 180 | x | + | | 80 | y | + | | 340 | z | = | | 20 | | (1) |
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Multiply both sides of equation (3) by 14 Divide both sides of equation (3) by 351, get the equation:, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
| | | | 180 | x | + | | 80 | y | + | | 340 | z | = | | 20 | | (1) |
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Multiply both sides of equation (3) by 34 Divide both sides of equation (3) by 39, 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 36, 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》 |