detailed information: The input equation set is:
| | | | 5 | x | + | | 25 | y | + | | 151 | z | = | | 136 | | (1) |
| | 25 | x | + | | 151 | y | + | | 1015 | z | = | | 940 | | (2) |
| | 151 | x | + | | 1015 | y | + | | 7219 | z | = | | 6766 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 5, the equation can be obtained: | | 25 | x | + | | 125 | y | + | | 755 | z | = | | 680 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | 5 | x | + | | 25 | y | + | | 151 | z | = | | 136 | | (1) |
| | | 151 | x | + | | 1015 | y | + | | 7219 | z | = | | 6766 | | (3) |
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Multiply both sides of equation (1) by 151 Divide the two sides of equation (1) by 5, the equation can be obtained: | | 151 | x | + | | 755 | y | + | | | 22801 5 | z | = | | | 20536 5 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | 5 | x | + | | 25 | y | + | | 151 | z | = | | 136 | | (1) |
| | | 260 | y | + | | | 13294 5 | z | = | | | 13294 5 | | (3) |
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Multiply both sides of equation (2) by 10, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | 5 | x | + | | 25 | y | + | | 151 | z | = | | 136 | | (1) |
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Multiply both sides of equation (3) by 650 Divide both sides of equation (3) by 147, get the equation:, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
| | | | 5 | x | + | | 25 | y | + | | 151 | z | = | | 136 | | (1) |
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Multiply both sides of equation (3) by 755 Divide both sides of equation (3) by 294, 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 25 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |