detailed information: The input equation set is: Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
Subtract both sides of equation (1) from both sides of equation (6) ,the equations are reduced to:
Add both sides of equation (2) to both sides of equation (3) ,the equations are reduced to:
Multiply both sides of equation (2) by 2, the equation can be obtained: , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
| | | | | | | 20 | C | + | | D | + | | 10 | E | + | | 2 | F | = | | | 77 5 | | (4) |
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Add both sides of equation (2) to both sides of equation (5) ,the equations are reduced to:
| | | | | | | 20 | C | + | | D | + | | 10 | E | + | | 2 | F | = | | | 77 5 | | (4) |
| | 10 | C | + | | 2 | D | + | | 5 | E | + | | F | = | | | 106 5 | | (5) |
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Subtract both sides of equation (2) from both sides of equation (6) ,the equations are reduced to:
| | | | | | | 20 | C | + | | D | + | | 10 | E | + | | 2 | F | = | | | 77 5 | | (4) |
| | 10 | C | + | | 2 | D | + | | 5 | E | + | | F | = | | | 106 5 | | (5) |
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Multiply both sides of equation (3) by 4 Divide the two sides of equation (3) by 3, the equation can be obtained: | | 20 | C | + | | | 4 3 | D | + | | | 4 3 | F | = | | | 82 5 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | | | - | 1 3 | D | + | | 10 | E | + | | | 2 3 | F | = | | -1 | | (4) |
| | 10 | C | + | | 2 | D | + | | 5 | E | + | | F | = | | | 106 5 | | (5) |
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Multiply both sides of equation (3) by 2 Divide the two sides of equation (3) by 3, the equation can be obtained: | | 10 | C | + | | | 2 3 | D | + | | | 2 3 | F | = | | | 41 5 | (9) | , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
| | | | | | - | 1 3 | D | + | | 10 | E | + | | | 2 3 | F | = | | -1 | | (4) |
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Multiply both sides of equation (3) by 2 Divide the two sides of equation (3) by 3, the equation can be obtained: | | 10 | C | + | | | 2 3 | D | + | | | 2 3 | F | = | | | 41 5 | (10) | , then add the two sides of equation (10) to both sides of equation (6), the equations are reduced to:
| | | | | | - | 1 3 | D | + | | 10 | E | + | | | 2 3 | F | = | | -1 | | (4) |
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Multiply both sides of equation (4) by 4, the equation can be obtained: | - | 4 3 | D | + | | 40 | E | + | | | 8 3 | F | = | | -4 | (11) | , then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
| | | | | | - | 1 3 | D | + | | 10 | E | + | | | 2 3 | F | = | | -1 | | (4) |
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Multiply both sides of equation (4) by 2, the equation can be obtained: | - | 2 3 | D | + | | 20 | E | + | | | 4 3 | F | = | | -2 | (12) | , then add the two sides of equation (12) to both sides of equation (6), the equations are reduced to:
| | | | | | - | 1 3 | D | + | | 10 | E | + | | | 2 3 | F | = | | -1 | | (4) |
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Multiply both sides of equation (5) by 4 Divide the two sides of equation (5) by 9, the equation can be obtained: , then subtract both sides of equation (13) from both sides of equation (6), the equations are reduced to:
| | | | | | - | 1 3 | D | + | | 10 | E | + | | | 2 3 | F | = | | -1 | | (4) |
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Multiply both sides of equation (6) by 9, get the equation:, then add the two sides of equation (14) to both sides of equation (5), get the equation:
| | | | | | - | 1 3 | D | + | | 10 | E | + | | | 2 3 | F | = | | -1 | | (4) |
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Multiply both sides of equation (6) by 2, get the equation:, then add the two sides of equation (15) to both sides of equation (4), get the equation:
Multiply both sides of equation (6) by 3, get the equation:, then add the two sides of equation (16) to both sides of equation (3), get the equation:
Multiply both sides of equation (6) by 3, get the equation:, then add the two sides of equation (17) to both sides of equation (2), get the equation:
Multiply both sides of equation (5) by 2 Divide both sides of equation (5) by 9, get the equation:, then subtract both sides of equation (18) from both sides of equation (4), get the equation:
Multiply both sides of equation (4) by 3, get the equation:, then add the two sides of equation (19) to both sides of equation (3), get the equation:
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 3, get the equation:, then subtract both sides of equation (20) from both sides of equation (2), get the equation:
Add both sides of equation (2) 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》 |