detailed information: The input equation set is:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| | 6 | A | + | | 6 | B | + | | C | + | | 2 | D | + | | 3 | E | + | | F | = | | | 6151 10 | | (2) |
| | 4 | A | + | | 6 | B | + | | C | + | | 2 | D | + | | 3 | E | + | | 2 | F | = | | | 2507 4 | | (3) |
| | 4 | A | + | | 4 | B | + | | C | + | | 2 | E | + | | F | = | | | 2507 5 | | (4) |
| | | Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| -1 | C | | -1 | E | | -1 | F | = | | - | 2507 10 | | (2) |
| | 4 | A | + | | 6 | B | + | | C | + | | 2 | D | + | | 3 | E | + | | 2 | F | = | | | 2507 4 | | (3) |
| | 4 | A | + | | 4 | B | + | | C | + | | 2 | E | + | | F | = | | | 2507 5 | | (4) |
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Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 3, the equation can be obtained: | | 4 | A | + | | 4 | B | + | | | 4 3 | C | + | | | 4 3 | D | + | | | 8 3 | E | + | | | 4 3 | F | = | | | 2886 5 | (7) | , then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| -1 | C | | -1 | E | | -1 | F | = | | - | 2507 10 | | (2) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | + | | | 2 3 | F | = | | | 991 20 | | (3) |
| | 4 | A | + | | 4 | B | + | | C | + | | 2 | E | + | | F | = | | | 2507 5 | | (4) |
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Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 3, the equation can be obtained: | | 4 | A | + | | 4 | B | + | | | 4 3 | C | + | | | 4 3 | D | + | | | 8 3 | E | + | | | 4 3 | F | = | | | 2886 5 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| -1 | C | | -1 | E | | -1 | F | = | | - | 2507 10 | | (2) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | + | | | 2 3 | F | = | | | 991 20 | | (3) |
| - | 1 3 | C | | - | 4 3 | D | | - | 2 3 | E | | - | 1 3 | F | = | | - | 379 5 | | (4) |
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Divide the two sides of equation (1) by 6, the equation can be obtained: | | A | + | | B | + | | | 1 3 | C | + | | | 1 3 | D | + | | | 2 3 | E | + | | | 1 3 | F | = | | | 1443 10 | (9) | , then subtract both sides of equation (9) from both sides of equation (6), the equations are reduced to:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| -1 | C | | -1 | E | | -1 | F | = | | - | 2507 10 | | (2) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | + | | | 2 3 | F | = | | | 991 20 | | (3) |
| - | 1 3 | C | | - | 4 3 | D | | - | 2 3 | E | | - | 1 3 | F | = | | - | 379 5 | | (4) |
| | -1 | B | | - | 1 3 | C | | - | 1 3 | D | | - | 2 3 | E | | - | 1 3 | F | = | | - | 1323 10 | | (6) |
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交After the exchange of equation (2) and equation (3), the equation system becomes:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | + | | | 2 3 | F | = | | | 991 20 | | (2) |
| -1 | C | | -1 | E | | -1 | F | = | | - | 2507 10 | | (3) |
| - | 1 3 | C | | - | 4 3 | D | | - | 2 3 | E | | - | 1 3 | F | = | | - | 379 5 | | (4) |
| | -1 | B | | - | 1 3 | C | | - | 1 3 | D | | - | 2 3 | E | | - | 1 3 | F | = | | - | 1323 10 | | (6) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: | | B | | - | 1 6 | C | + | | | 1 3 | D | + | | | 1 6 | E | + | | | 1 3 | F | = | | | 991 40 | (10) | , then add the two sides of equation (10) to both sides of equation (6), the equations are reduced to:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | + | | | 2 3 | F | = | | | 991 20 | | (2) |
| -1 | C | | -1 | E | | -1 | F | = | | - | 2507 10 | | (3) |
| - | 1 3 | C | | - | 4 3 | D | | - | 2 3 | E | | - | 1 3 | F | = | | - | 379 5 | | (4) |
| | - | 1 2 | C | | - | 1 2 | E | = | | - | 4301 40 | | (6) |
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Divide the two sides of equation (3) by 3, the equation can be obtained: | - | 1 3 | C | | - | 1 3 | E | | - | 1 3 | F | = | | - | 2507 30 | (11) | , then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | + | | | 2 3 | F | = | | | 991 20 | | (2) |
| -1 | C | | -1 | E | | -1 | F | = | | - | 2507 10 | | (3) |
| | | - | 1 2 | C | | - | 1 2 | E | = | | - | 4301 40 | | (6) |
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Divide the two sides of equation (3) by 2, the equation can be obtained: | - | 1 2 | C | | - | 1 2 | E | | - | 1 2 | F | = | | - | 2507 20 | (12) | , then subtract both sides of equation (12) from both sides of equation (6), the equations are reduced to:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | + | | | 2 3 | F | = | | | 991 20 | | (2) |
| -1 | C | | -1 | E | | -1 | F | = | | - | 2507 10 | | (3) |
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Multiply both sides of equation (6) by 2, get the equation:, then add the two sides of equation (13) to both sides of equation (3), get the equation:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | + | | | 2 3 | F | = | | | 991 20 | | (2) |
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Multiply both sides of equation (6) by 4 Divide both sides of equation (6) by 3, get the equation:, then subtract both sides of equation (14) from both sides of equation (2), get the equation:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | + | | 2 | F | = | | | 4329 5 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | = | | | 1547 60 | | (2) |
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Multiply both sides of equation (6) by 4, get the equation:, then subtract both sides of equation (15) from both sides of equation (1), get the equation:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | = | | | 1589 2 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | = | | | 1547 60 | | (2) |
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Divide both sides of equation (5) by 3, get the equation:, then add the two sides of equation (16) to both sides of equation (4), get the equation:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | = | | | 1589 2 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | = | | | 1547 60 | | (2) |
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Add both sides of equation (5) to both sides of equation (3), get the equation:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | = | | | 1589 2 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | + | | | 1 3 | E | = | | | 1547 60 | | (2) |
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Divide both sides of equation (5) by 3, get the equation:, then subtract both sides of equation (17) from both sides of equation (2), get the equation:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | + | | 4 | E | = | | | 1589 2 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | = | | | 349 20 | | (2) |
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Multiply both sides of equation (5) by 4, get the equation:, then subtract both sides of equation (18) from both sides of equation (1), get the equation:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | = | | | 1389 2 | | (1) |
| | 2 | B | | - | 1 3 | C | + | | | 2 3 | D | = | | | 349 20 | | (2) |
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Divide both sides of equation (4) by 2, get the equation:, then add the two sides of equation (19) to both sides of equation (2), get the equation:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | + | | 2 | D | = | | | 1389 2 | | (1) |
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Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 2, get the equation:, then add the two sides of equation (20) to both sides of equation (1), get the equation:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | = | | | 14373 20 | | (1) |
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Divide both sides of equation (3) by 3, get the equation:, then subtract both sides of equation (21) from both sides of equation (2), get the equation:
 | | | | 6 | A | + | | 6 | B | + | | 2 | C | = | | | 14373 20 | | (1) |
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Multiply both sides of equation (3) by 2, get the equation:, then add the two sides of equation (22) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 3, get the equation:, then subtract both sides of equation (23) from 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》 |