detailed information: The input equation set is: Question solving process:
Multiply both sides of equation (1) 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:
Multiply both sides of equation (1) 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:
Multiply both sides of equation (2) by 2, the equation can be obtained: , then add the two sides of equation (9) to both sides of equation (3), the equations are reduced to:
Add both sides of equation (2) to both sides of equation (6) ,the equations are reduced to:
Divide the two sides of equation (3) by 3, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | | | | | 11 3 | D | | - | 4 3 | E | + | | 3 | F | = | | | 52 3 | | (4) |
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Divide the two sides of equation (3) by 3, the equation can be obtained: , then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
| | | | | | | | 11 3 | D | | - | 4 3 | E | + | | 3 | F | = | | | 52 3 | | (4) |
| | - | 1 3 | D | + | | | 2 3 | E | + | | F | = | | - | 2 3 | | (6) |
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Multiply both sides of equation (4) by 6 Divide the two sides of equation (4) by 11, the equation can be obtained: | | 2 | D | | - | 8 11 | E | + | | | 18 11 | F | = | | | 104 11 | (12) | , then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
| | | | | | | | 11 3 | D | | - | 4 3 | E | + | | 3 | F | = | | | 52 3 | | (4) |
| | - | 1 3 | D | + | | | 2 3 | E | + | | F | = | | - | 2 3 | | (6) |
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Divide the two sides of equation (4) by 11, the equation can be obtained: | | | 1 3 | D | | - | 4 33 | E | + | | | 3 11 | F | = | | | 52 33 | (13) | , then add the two sides of equation (13) to both sides of equation (6), the equations are reduced to:
| | | | | | | | 11 3 | D | | - | 4 3 | E | + | | 3 | F | = | | | 52 3 | | (4) |
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Multiply both sides of equation (5) by 6 Divide the two sides of equation (5) by 19, the equation can be obtained: | | | 6 11 | E | | - | 108 209 | F | = | | | 564 209 | (14) | , then subtract both sides of equation (14) from both sides of equation (6), the equations are reduced to:
| | | | | | | | 11 3 | D | | - | 4 3 | E | + | | 3 | F | = | | | 52 3 | | (4) |
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Multiply both sides of equation (6) by 171 Divide both sides of equation (6) by 187, get the equation:, then add the two sides of equation (15) to both sides of equation (5), get the equation:
| | | | | | | | 11 3 | D | | - | 4 3 | E | + | | 3 | F | = | | | 52 3 | | (4) |
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Multiply both sides of equation (6) by 57 Divide both sides of equation (6) by 34, get the equation:, then subtract both sides of equation (16) from both sides of equation (4), get the equation:
Multiply both sides of equation (5) by 44 Divide both sides of equation (5) by 57, get the equation:, then add the two sides of equation (17) to both sides of equation (4), get the equation:
Multiply both sides of equation (5) by 44 Divide both sides of equation (5) by 19, get the equation:, then subtract both sides of equation (18) from both sides of equation (3), get the equation:
Multiply both sides of equation (5) by 22 Divide both sides of equation (5) by 19, get the equation:, then subtract both sides of equation (19) from both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 11, get the equation:, then subtract both sides of equation (20) from both sides of equation (3), 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |