detailed information: The input equation set is:
 | | | | 158000 | A | + | | 739417 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 28232 | | (1) |
| | 158000 | A | + | | 781537 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 28867 | | (2) |
| | 285000 | A | + | | 1934379 | B | + | | 549000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 47944 | | (3) |
| | 158000 | A | + | | 1327909 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37095 | | (4) |
| | 158000 | A | + | | 1330509 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37134 | | (5) |
| | 158000 | A | + | | 1327909 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37095 | | (6) |
| Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 | | | | 158000 | A | + | | 739417 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 28232 | | (1) |
| | | 285000 | A | + | | 1934379 | B | + | | 549000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 47944 | | (3) |
| | 158000 | A | + | | 1327909 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37095 | | (4) |
| | 158000 | A | + | | 1330509 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37134 | | (5) |
| | 158000 | A | + | | 1327909 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37095 | | (6) |
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Multiply both sides of equation (1) by 285 Divide the two sides of equation (1) by 158, the equation can be obtained: | | 285000 | A | + | | | 210733845 158 | B | + | | | 65407500 79 | C | + | | | 62415000 79 | D | + | | | 7125000 79 | E | + | | | 39187500 79 | F | = | | | 4023060 79 | (7) | , then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 | | | | 158000 | A | + | | 739417 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 28232 | | (1) |
| | | | 94898037 158 | B | | - | 22036500 79 | C | | - | 27813000 79 | D | | - | 3175000 79 | E | | - | 17462500 79 | F | = | | - | 235484 79 | | (3) |
| | 158000 | A | + | | 1327909 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37095 | | (4) |
| | 158000 | A | + | | 1330509 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37134 | | (5) |
| | 158000 | A | + | | 1327909 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37095 | | (6) |
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Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
 | | | | 158000 | A | + | | 739417 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 28232 | | (1) |
| | | | 94898037 158 | B | | - | 22036500 79 | C | | - | 27813000 79 | D | | - | 3175000 79 | E | | - | 17462500 79 | F | = | | - | 235484 79 | | (3) |
| | | 158000 | A | + | | 1330509 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37134 | | (5) |
| | 158000 | A | + | | 1327909 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37095 | | (6) |
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Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
 | | | | 158000 | A | + | | 739417 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 28232 | | (1) |
| | | | 94898037 158 | B | | - | 22036500 79 | C | | - | 27813000 79 | D | | - | 3175000 79 | E | | - | 17462500 79 | F | = | | - | 235484 79 | | (3) |
| | | | 158000 | A | + | | 1327909 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 37095 | | (6) |
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Subtract both sides of equation (1) from both sides of equation (6) ,the equations are reduced to:
 | | | | 158000 | A | + | | 739417 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 28232 | | (1) |
| | | | 94898037 158 | B | | - | 22036500 79 | C | | - | 27813000 79 | D | | - | 3175000 79 | E | | - | 17462500 79 | F | = | | - | 235484 79 | | (3) |
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Multiply both sides of equation (2) by 2433283 Divide the two sides of equation (2) by 170640, the equation can be obtained: | | | 94898037 158 | B | = | | | 309026941 34128 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 | | | | 158000 | A | + | | 739417 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 28232 | | (1) |
| | - | 22137484 10665 | C | | - | 42296 135 | D | | - | 108245912 10665 | E | | - | 6497956 1185 | F | = | | - | 410756029 34128 | | (3) |
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Multiply both sides of equation (2) by 5449 Divide the two sides of equation (2) by 390, the equation can be obtained: , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 | | | | 158000 | A | + | | 739417 | B | + | | 459000 | C | + | | 438000 | D | + | | 50000 | E | + | | 275000 | F | = | | 28232 | | (1) |
| | - | 22137484 10665 | C | | - | 42296 135 | D | | - | 108245912 10665 | E | | - | 6497956 1185 | F | = | | - | 410756029 34128 | | (3) |
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由第(4)方程式可以看出,该方程组无解。
解方程组的详细方法请参阅:《多元一次方程组的解法》 |