detailed information: The input equation set is:
 | | | | | 1000000 | x | + | | 1000 | y | + | | 100 | z | = | | -1 | | (1) |
| | | 27000000 | x | + | | 90000 | y | + | | 300 | z | = | | -2 | | (2) |
| | | 148877000 | x | + | | 280900 | y | + | | 530 | z | = | | -2 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 27, the equation can be obtained: | | | 27000000 | x | + | | 27000 | y | + | | 2700 | z | = | | -27 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 | | | | | 1000000 | x | + | | 1000 | y | + | | 100 | z | = | | -1 | | (1) |
| | | | 148877000 | x | + | | 280900 | y | + | | 530 | z | = | | -2 | | (3) |
|
Multiply both sides of equation (1) by 148877 Divide the two sides of equation (1) by 1000, the equation can be obtained: | | | 148877000 | x | + | | 148877 | y | + | | | 148877 10 | z | = | | - | 148877 1000 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 | | | | | 1000000 | x | + | | 1000 | y | + | | 100 | z | = | | -1 | | (1) |
| | | | 132023 | y | | - | 143577 10 | z | = | | | 146877 1000 | | (3) |
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Multiply both sides of equation (2) by 132023 Divide the two sides of equation (2) by 63000, the equation can be obtained: | | | 132023 | y | | - | 528092 105 | z | = | | | 132023 2520 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 | | | | | 1000000 | x | + | | 1000 | y | + | | 100 | z | = | | -1 | | (1) |
| | | - | 1958933 210 | z | = | | | 1488169 15750 | | (3) |
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Multiply both sides of equation (3) by 504000 Divide both sides of equation (3) by 1958933, get the equation:| | - | 3856800 1607 | z | = | | | 2070496 85171 | (7) | , then subtract both sides of equation (7) from both sides of equation (2), get the equation:
 | | | | | 1000000 | x | + | | 1000 | y | + | | 100 | z | = | | -1 | | (1) |
| | | - | 1958933 210 | z | = | | | 1488169 15750 | | (3) |
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Multiply both sides of equation (3) by 21000 Divide both sides of equation (3) by 1958933, get the equation:| | - | 160700 1607 | z | = | | | 258812 255513 | (8) | , then add the two sides of equation (8) to both sides of equation (1), get the equation:
 | | | | | 1000000 | x | + | | 1000 | y | = | | | 3299 255513 | | (1) |
| | | - | 1958933 210 | z | = | | | 1488169 15750 | | (3) |
|
Divide both sides of equation (2) by 63, get the equation:, then subtract both sides of equation (9) from both sides of equation (1), get the equation:
 | | | | | 1000000 | x | = | | | 803500 410609391 | | (1) |
| | |
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》 |