detailed information: The input equation set is:
 | | | | | 399 5000 | x | + | | | 1399 5000 | y | + | | | 1399 5000 | z | = | | | 6279 1000 | | (1) |
| | | 279 1000 | x | + | | | 279 1000 | y | + | | | 279 1000 | z | = | | | 6279 1000 | | (2) |
| | | 279 1000 | x | + | | | 279 1000 | y | + | | | 279 1000 | z | = | | | 6279 1000 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 465 Divide the two sides of equation (1) by 133, the equation can be obtained: | | | 279 1000 | x | + | | | 130107 133000 | y | + | | | 130107 133000 | z | = | | | 83421 3800 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 | | | | | 399 5000 | x | + | | | 1399 5000 | y | + | | | 1399 5000 | z | = | | | 6279 1000 | | (1) |
| - | 93 133 | y | | - | 93 133 | z | = | | - | 74451 4750 | | (2) |
| | | 279 1000 | x | + | | | 279 1000 | y | + | | | 279 1000 | z | = | | | 6279 1000 | | (3) |
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Multiply both sides of equation (1) by 465 Divide the two sides of equation (1) by 133, the equation can be obtained: | | | 279 1000 | x | + | | | 130107 133000 | y | + | | | 130107 133000 | z | = | | | 83421 3800 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 | | | | | 399 5000 | x | + | | | 1399 5000 | y | + | | | 1399 5000 | z | = | | | 6279 1000 | | (1) |
| - | 93 133 | y | | - | 93 133 | z | = | | - | 74451 4750 | | (2) |
| - | 93 133 | y | | - | 93 133 | z | = | | - | 74451 4750 | | (3) |
|
Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
 | | | | | 399 5000 | x | + | | | 1399 5000 | y | + | | | 1399 5000 | z | = | | | 6279 1000 | | (1) |
| - | 93 133 | y | | - | 93 133 | z | = | | - | 74451 4750 | | (2) |
| |
Multiply both sides of equation (2) by 186067 Divide both sides of equation (2) by 465000, get the equation: | - | 1399 5000 | y | | - | 1399 5000 | z | = | | - | 243032881 38750000 | (6) | , then add the two sides of equation (6) to both sides of equation (1), get the equation:
 | | | | | 399 5000 | x | = | | | 278369 38750000 | | (1) |
| - | 93 133 | y | | - | 93 133 | z | = | | - | 74451 4750 | | (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:
Where: z are arbitrary constants. 解方程组的详细方法请参阅:《多元一次方程组的解法》 |