detailed information: The input equation set is:
| | | | | 111 500 | x | + | | | 4 125 | y | + | | | 629 125 | z | = | | | 103 100 | | (1) |
| | | 3 100 | x | + | | | 3 100 | y | + | | | 603 100 | z | = | | 1 | | (2) |
| | Question solving process:
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 37, the equation can be obtained: | | | 3 100 | x | + | | | 4 925 | y | + | | | 17 25 | z | = | | | 103 740 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | | 111 500 | x | + | | | 4 125 | y | + | | | 629 125 | z | = | | | 103 100 | | (1) |
| | | 19 740 | y | + | | | 107 20 | z | = | | | 637 740 | | (2) |
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Multiply both sides of equation (1) by 500 Divide the two sides of equation (1) by 111, the equation can be obtained: | | x | + | | | 16 111 | y | + | | | 2516 111 | z | = | | | 515 111 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | | 111 500 | x | + | | | 4 125 | y | + | | | 629 125 | z | = | | | 103 100 | | (1) |
| | | 19 740 | y | + | | | 107 20 | z | = | | | 637 740 | | (2) |
| - | 16 111 | y | | - | 2183 111 | z | = | | | 373 111 | | (3) |
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Multiply both sides of equation (2) by 11840 Divide the two sides of equation (2) by 2109, the equation can be obtained: | | | 16 111 | y | + | | | 1712 57 | z | = | | | 10192 2109 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | | | 111 500 | x | + | | | 4 125 | y | + | | | 629 125 | z | = | | | 103 100 | | (1) |
| | | 19 740 | y | + | | | 107 20 | z | = | | | 637 740 | | (2) |
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Multiply both sides of equation (3) by 75221 Divide both sides of equation (3) by 145780, get the equation: | | | 21079 3940 | z | = | | | 49969 11820 | (7) | , then subtract both sides of equation (7) from both sides of equation (2), get the equation:
| | | | | 111 500 | x | + | | | 4 125 | y | + | | | 629 125 | z | = | | | 103 100 | | (1) |
| | | 19 740 | y | = | | - | 736193 218670 | | (2) |
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Multiply both sides of equation (3) by 442187 Divide both sides of equation (3) by 911125, get the equation: | | | 123913 24625 | z | = | | | 293743 73875 | (8) | , then subtract both sides of equation (8) from both sides of equation (1), get the equation:
| | | | | 111 500 | x | + | | | 4 125 | y | = | | - | 870607 295500 | | (1) |
| | | 19 740 | y | = | | - | 736193 218670 | | (2) |
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Multiply both sides of equation (2) by 592 Divide both sides of equation (2) by 475, get the equation: | | | 148 4625 | y | = | | - | 309976 73875 | (9) | , then subtract both sides of equation (9) from both sides of equation (1), get the equation:
| | | | | 111 500 | x | = | | | 123099 98500 | | (1) |
| | | 19 740 | y | = | | - | 736193 218670 | | (2) |
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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》 |