detailed information: The input equation set is:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| | A | + | | | 9 10 | B | + | | 19 | C | + | | 9 | D | + | | 7 | E | = | | | 7 5 | | (2) |
| | A | + | | | 4 5 | B | + | | | 104 5 | C | + | | | 54 5 | D | + | | | 34 5 | E | = | | | 9 5 | | (3) |
| | A | + | | | 4 5 | B | + | | | 114 5 | C | + | | | 54 5 | D | + | | 6 | E | = | | | 9 5 | | (4) |
| | A | + | | | 4 5 | B | + | | 24 | C | + | | | 54 5 | D | + | | | 29 5 | E | = | | | 9 5 | | (5) |
| Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| | A | + | | | 4 5 | B | + | | | 104 5 | C | + | | | 54 5 | D | + | | | 34 5 | E | = | | | 9 5 | | (3) |
| | A | + | | | 4 5 | B | + | | | 114 5 | C | + | | | 54 5 | D | + | | 6 | E | = | | | 9 5 | | (4) |
| | A | + | | | 4 5 | B | + | | 24 | C | + | | | 54 5 | D | + | | | 29 5 | E | = | | | 9 5 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| - | 1 5 | B | + | | | 19 5 | C | + | | | 9 5 | D | | - | 7 10 | E | = | | | 2 5 | | (3) |
| | A | + | | | 4 5 | B | + | | | 114 5 | C | + | | | 54 5 | D | + | | 6 | E | = | | | 9 5 | | (4) |
| | A | + | | | 4 5 | B | + | | 24 | C | + | | | 54 5 | D | + | | | 29 5 | E | = | | | 9 5 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| - | 1 5 | B | + | | | 19 5 | C | + | | | 9 5 | D | | - | 7 10 | E | = | | | 2 5 | | (3) |
| - | 1 5 | B | + | | | 29 5 | C | + | | | 9 5 | D | | - | 3 2 | E | = | | | 2 5 | | (4) |
| | A | + | | | 4 5 | B | + | | 24 | C | + | | | 54 5 | D | + | | | 29 5 | E | = | | | 9 5 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| - | 1 5 | B | + | | | 19 5 | C | + | | | 9 5 | D | | - | 7 10 | E | = | | | 2 5 | | (3) |
| - | 1 5 | B | + | | | 29 5 | C | + | | | 9 5 | D | | - | 3 2 | E | = | | | 2 5 | | (4) |
| - | 1 5 | B | + | | 7 | C | + | | | 9 5 | D | | - | 17 10 | E | = | | | 2 5 | | (5) |
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Multiply both sides of equation (2) by 2, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| - | 1 5 | C | + | | | 9 5 | D | + | | | 3 10 | E | = | | | 2 5 | | (3) |
| - | 1 5 | B | + | | | 29 5 | C | + | | | 9 5 | D | | - | 3 2 | E | = | | | 2 5 | | (4) |
| - | 1 5 | B | + | | 7 | C | + | | | 9 5 | D | | - | 17 10 | E | = | | | 2 5 | | (5) |
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Multiply both sides of equation (2) by 2, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| - | 1 5 | C | + | | | 9 5 | D | + | | | 3 10 | E | = | | | 2 5 | | (3) |
| | - | 1 5 | B | + | | 7 | C | + | | | 9 5 | D | | - | 17 10 | E | = | | | 2 5 | | (5) |
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Multiply both sides of equation (2) by 2, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| - | 1 5 | C | + | | | 9 5 | D | + | | | 3 10 | E | = | | | 2 5 | | (3) |
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Multiply both sides of equation (3) by 9, the equation can be obtained: | - | 9 5 | C | + | | | 81 5 | D | + | | | 27 10 | E | = | | | 18 5 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| - | 1 5 | C | + | | | 9 5 | D | + | | | 3 10 | E | = | | | 2 5 | | (3) |
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Multiply both sides of equation (3) by 15, the equation can be obtained: , then add the two sides of equation (10) to both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| - | 1 5 | C | + | | | 9 5 | D | + | | | 3 10 | E | = | | | 2 5 | | (3) |
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Multiply both sides of equation (4) by 8 Divide the two sides of equation (4) by 5, the equation can be obtained: , then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| - | 1 5 | C | + | | | 9 5 | D | + | | | 3 10 | E | = | | | 2 5 | | (3) |
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Multiply both sides of equation (5) by 55 Divide both sides of equation (5) by 7, get the equation:, then subtract both sides of equation (12) from both sides of equation (4), get the equation:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
| - | 1 5 | C | + | | | 9 5 | D | + | | | 3 10 | E | = | | | 2 5 | | (3) |
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Multiply both sides of equation (5) by 15 Divide both sides of equation (5) by 14, get the equation:, then subtract both sides of equation (13) from both sides of equation (3), get the equation:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
| - | 1 10 | B | + | | 2 | C | | - | 1 2 | E | = | | 0 | | (2) |
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Multiply both sides of equation (5) by 25 Divide both sides of equation (5) by 14, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | + | | | 15 2 | E | = | | | 7 5 | | (1) |
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Multiply both sides of equation (5) by 375 Divide both sides of equation (5) by 14, get the equation:, then subtract both sides of equation (15) from both sides of equation (1), get the equation:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | = | | | 7 5 | | (1) |
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Divide both sides of equation (4) by 10, get the equation:, then subtract both sides of equation (16) from both sides of equation (3), get the equation:
| | | | A | + | | B | + | | 17 | C | + | | 9 | D | = | | | 7 5 | | (1) |
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Divide both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (17) from both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 10, get the equation:, then add the two sides of equation (18) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 85, get the equation:, then add the two sides of equation (19) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 10, get the equation:, then add the two sides of equation (20) 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》 |