detailed information: The input equation set is:
| | | | 400 | x | + | | 200 | y | + | | 100 | z | = | | 38 | | (1) |
| | 800 | x | + | | 200 | y | + | | 50 | z | = | | 19 | | (2) |
| | Question solving process:
Multiply both sides of equation (1) by 2, the equation can be obtained: | | 800 | x | + | | 400 | y | + | | 200 | z | = | | 76 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | 400 | x | + | | 200 | y | + | | 100 | z | = | | 38 | | (1) |
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Divide the two sides of equation (1) by 16, the equation can be obtained: | | 25 | x | + | | | 25 2 | y | + | | | 25 4 | z | = | | | 19 8 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | 400 | x | + | | 200 | y | + | | 100 | z | = | | 38 | | (1) |
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Multiply both sides of equation (2) by 3 Divide the two sides of equation (2) by 80, the equation can be obtained: | - | 15 2 | y | | - | 45 8 | z | = | | - | 171 80 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | 400 | x | + | | 200 | y | + | | 100 | z | = | | 38 | | (1) |
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Multiply both sides of equation (3) by 400, get the equation:, then add the two sides of equation (7) to both sides of equation (2), get the equation:
| | | | 400 | x | + | | 200 | y | + | | 100 | z | = | | 38 | | (1) |
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Multiply both sides of equation (3) by 800 Divide both sides of equation (3) by 3, get the equation:, then subtract both sides of equation (8) from both sides of equation (1), get the equation:
| | | | 400 | x | + | | 200 | y | = | | - | 4496 3 | | (1) |
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Add both sides of equation (2) 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》 |