detailed information: The input equation set is:
| | | | | 13 8 | x | + | | | 3 4 | y | + | | | 3 4 | z | = | | 180 | | (1) |
| | | | 3 4 | x | + | | | 11 4 | y | + | | | 3 4 | z | = | | 180 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 8 Divide the two sides of equation (1) by 13, the equation can be obtained: | | x | + | | | 6 13 | y | + | | | 6 13 | z | = | | | 1440 13 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | | 13 8 | x | + | | | 3 4 | y | + | | | 3 4 | z | = | | 180 | | (1) |
| | | | 3 4 | x | + | | | 11 4 | y | + | | | 3 4 | z | = | | 180 | | (3) |
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Multiply both sides of equation (1) by 6 Divide the two sides of equation (1) by 13, the equation can be obtained: | | | 3 4 | x | + | | | 9 26 | y | + | | | 9 26 | z | = | | | 1080 13 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | | 13 8 | x | + | | | 3 4 | y | + | | | 3 4 | z | = | | 180 | | (1) |
| | | | 125 52 | y | + | | | 21 52 | z | = | | | 1260 13 | | (3) |
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Multiply both sides of equation (2) by 25 Divide the two sides of equation (2) by 16, the equation can be obtained: | | | 125 52 | y | | - | 75 104 | z | = | | | 5625 52 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | 13 8 | x | + | | | 3 4 | y | + | | | 3 4 | z | = | | 180 | | (1) |
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Multiply both sides of equation (3) by 16 Divide both sides of equation (3) by 39, get the equation:, then add the two sides of equation (7) to both sides of equation (2), get the equation:
| | | | | 13 8 | x | + | | | 3 4 | y | + | | | 3 4 | z | = | | 180 | | (1) |
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Multiply both sides of equation (3) by 26 Divide both sides of equation (3) by 39, 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 39 Divide both sides of equation (2) by 80, 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |