detailed information: The input equation set is:
| | | | x | + | | | 6063 20 | y | + | | 91 | z | = | | | 39 100000 | | (1) |
| | x | + | | | 30803 100 | y | + | | 94 | z | = | | | 3 100 | | (2) |
| | x | + | | | 31303 100 | y | + | | 98 | z | = | | | 3 100 | | (3) |
| Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | x | + | | | 6063 20 | y | + | | 91 | z | = | | | 39 100000 | | (1) |
| | | 122 25 | y | + | | 3 | z | = | | | 2961 100000 | | (2) |
| | x | + | | | 31303 100 | y | + | | 98 | z | = | | | 3 100 | | (3) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | x | + | | | 6063 20 | y | + | | 91 | z | = | | | 39 100000 | | (1) |
| | | 122 25 | y | + | | 3 | z | = | | | 2961 100000 | | (2) |
| | | 247 25 | y | + | | 7 | z | = | | | 2961 100000 | | (3) |
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Multiply both sides of equation (2) by 247 Divide the two sides of equation (2) by 122, the equation can be obtained: | | | 247 25 | y | + | | | 741 122 | z | = | | | 731367 12200000 | (4) | , then subtract both sides of equation (4) from both sides of equation (3), the equations are reduced to:
| | | | x | + | | | 6063 20 | y | + | | 91 | z | = | | | 39 100000 | | (1) |
| | | 122 25 | y | + | | 3 | z | = | | | 2961 100000 | | (2) |
| | | 113 122 | z | = | | - | 2961 97600 | | (3) |
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Multiply both sides of equation (3) by 366 Divide both sides of equation (3) by 113, get the equation: | | | 339 113 | z | = | | - | 8883 90400 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), get the equation:
| | | | x | + | | | 6063 20 | y | + | | 91 | z | = | | | 39 100000 | | (1) |
| | | 122 25 | y | = | | | 180621 1412500 | | (2) |
| | | 113 122 | z | = | | - | 2961 97600 | | (3) |
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Multiply both sides of equation (3) by 11102 Divide both sides of equation (3) by 113, get the equation: | | | 10283 113 | z | = | | - | 269451 90400 | (6) | , then subtract both sides of equation (6) from both sides of equation (1), get the equation:
| | | | x | + | | | 6063 20 | y | = | | | 16842891 5650000 | | (1) |
| | | 122 25 | y | = | | | 180621 1412500 | | (2) |
| | | 113 122 | z | = | | - | 2961 97600 | | (3) |
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Multiply both sides of equation (2) by 30315 Divide both sides of equation (2) by 488, get the equation: | | | 6063 20 | y | = | | | 17952543 2260000 | (7) | , then subtract both sides of equation (7) from both sides of equation (1), get the equation:
| | | | x | = | | - | 2041726133 1276900000 | | (1) |
| | | 122 25 | y | = | | | 180621 1412500 | | (2) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
| | | | x | = | | - | 2041726133 1276900000 | | (1) |
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Therefore, the solution of the equation set is:
| | | x = | | - | 2041726133 1276900000 | | | | | Question solving process:
Multiply both sides of equation (1) by 2, the equation can be obtained: , then subtract both sides of equation (3) from both sides of equation (2), the equations are reduced to:
由第(2)方程式可以看出,该方程组无解。
解方程组的详细方法请参阅:《多元一次方程组的解法》 |
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