detailed information: The input equation set is:
| | | | | 7 2 | x | + | | | 3 2 | y | + | | | 6 5 | z | = | | | 1836 5 | | (1) |
| | | 3 2 | x | + | | | 5 2 | y | + | | | 5 2 | z | = | | | 749 2 | | (2) |
| | | 3 2 | x | + | | | 3 2 | y | + | | | 1 2 | z | = | | | 411 2 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 7, the equation can be obtained: | | | 3 2 | x | + | | | 9 14 | y | + | | | 18 35 | z | = | | | 5508 35 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | | 7 2 | x | + | | | 3 2 | y | + | | | 6 5 | z | = | | | 1836 5 | | (1) |
| | | 13 7 | y | + | | | 139 70 | z | = | | | 15199 70 | | (2) |
| | | 3 2 | x | + | | | 3 2 | y | + | | | 1 2 | z | = | | | 411 2 | | (3) |
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Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 7, the equation can be obtained: | | | 3 2 | x | + | | | 9 14 | y | + | | | 18 35 | z | = | | | 5508 35 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | | 7 2 | x | + | | | 3 2 | y | + | | | 6 5 | z | = | | | 1836 5 | | (1) |
| | | 13 7 | y | + | | | 139 70 | z | = | | | 15199 70 | | (2) |
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Multiply both sides of equation (2) by 6 Divide the two sides of equation (2) by 13, the equation can be obtained: | | | 6 7 | y | + | | | 417 455 | z | = | | | 45597 455 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | 7 2 | x | + | | | 3 2 | y | + | | | 6 5 | z | = | | | 1836 5 | | (1) |
| | | 13 7 | y | + | | | 139 70 | z | = | | | 15199 70 | | (2) |
| - | 121 130 | z | = | | - | 6771 130 | | (3) |
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Multiply both sides of equation (3) by 1807 Divide both sides of equation (3) by 847, get the equation: | - | 139 70 | z | = | | - | 941169 8470 | (7) | , then add the two sides of equation (7) to both sides of equation (2), get the equation:
| | | | | 7 2 | x | + | | | 3 2 | y | + | | | 6 5 | z | = | | | 1836 5 | | (1) |
| | - | 121 130 | z | = | | - | 6771 130 | | (3) |
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Multiply both sides of equation (3) by 156 Divide both sides of equation (3) by 121, get the equation:, then add the two sides of equation (8) to both sides of equation (1), get the equation:
| | | | | - | 121 130 | z | = | | - | 6771 130 | | (3) |
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Multiply both sides of equation (2) by 21 Divide both sides of equation (2) by 26, 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》 |