detailed information: The input equation set is:
 | | | | 361 | x | + | | 19 | y | + | | z | = | | | 1387 5 | | (1) |
| | | 441 | x | + | | 21 | y | + | | z | = | | | 1911 5 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 400 Divide the two sides of equation (1) by 361, the equation can be obtained: | | 400 | x | + | | | 400 19 | y | + | | | 400 361 | z | = | | | 5840 19 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 | | | | 361 | x | + | | 19 | y | + | | z | = | | | 1387 5 | | (1) |
| - | 20 19 | y | | - | 39 361 | z | = | | | 392 19 | | (2) |
| | 441 | x | + | | 21 | y | + | | z | = | | | 1911 5 | | (3) |
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Multiply both sides of equation (1) by 441 Divide the two sides of equation (1) by 361, the equation can be obtained: | | 441 | x | + | | | 441 19 | y | + | | | 441 361 | z | = | | | 32193 95 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 | | | | 361 | x | + | | 19 | y | + | | z | = | | | 1387 5 | | (1) |
| - | 20 19 | y | | - | 39 361 | z | = | | | 392 19 | | (2) |
| - | 42 19 | y | | - | 80 361 | z | = | | | 4116 95 | | (3) |
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Multiply both sides of equation (2) by 21 Divide the two sides of equation (2) by 10, the equation can be obtained: | - | 42 19 | y | | - | 819 3610 | z | = | | | 4116 95 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 | | | | 361 | x | + | | 19 | y | + | | z | = | | | 1387 5 | | (1) |
| - | 20 19 | y | | - | 39 361 | z | = | | | 392 19 | | (2) |
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Multiply both sides of equation (3) by 7410 Divide both sides of equation (3) by 361, get the equation:, then add the two sides of equation (7) to both sides of equation (2), get the equation:
 | | | | 361 | x | + | | 19 | y | + | | z | = | | | 1387 5 | | (1) |
| | |
Multiply both sides of equation (3) by 190, 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 361 Divide both sides of equation (2) by 20, get the equation:, then add the two sides of equation (9) to 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》 |