detailed information: The input equation set is: Question solving process:
Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 3, the equation can be obtained: , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
| | | | | | 19 3 | B | | -3 | C | | - | 4 3 | D | = | | | 130 3 | | (2) |
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Divide the two sides of equation (1) by 3, the equation can be obtained: , then add the two sides of equation (6) to both sides of equation (4), the equations are reduced to:
| | | | | | 19 3 | B | | -3 | C | | - | 4 3 | D | = | | | 130 3 | | (2) |
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Multiply both sides of equation (2) by 3 Divide the two sides of equation (2) by 19, the equation can be obtained: | | B | | - | 9 19 | C | | - | 4 19 | D | = | | | 130 19 | (7) | , then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
| | | | | | 19 3 | B | | -3 | C | | - | 4 3 | D | = | | | 130 3 | | (2) |
| | | 10 19 | C | | - | 4 19 | D | = | | | 1042 19 | | (3) |
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Divide the two sides of equation (2) by 19, the equation can be obtained: | | | 1 3 | B | | - | 3 19 | C | | - | 4 57 | D | = | | | 130 57 | (8) | , then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
| | | | | | 19 3 | B | | -3 | C | | - | 4 3 | D | = | | | 130 3 | | (2) |
| | | 10 19 | C | | - | 4 19 | D | = | | | 1042 19 | | (3) |
| - | 3 19 | C | + | | | 5 19 | D | = | | - | 286 19 | | (4) |
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Multiply both sides of equation (3) by 3 Divide the two sides of equation (3) by 10, the equation can be obtained: , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | | | 19 3 | B | | -3 | C | | - | 4 3 | D | = | | | 130 3 | | (2) |
| | | 10 19 | C | | - | 4 19 | D | = | | | 1042 19 | | (3) |
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Multiply both sides of equation (4) by 20 Divide both sides of equation (4) by 19, get the equation:, then add the two sides of equation (10) to both sides of equation (3), get the equation:
| | | | | | 19 3 | B | | -3 | C | | - | 4 3 | D | = | | | 130 3 | | (2) |
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Multiply both sides of equation (4) by 20 Divide both sides of equation (4) by 3, get the equation:, then add the two sides of equation (11) to both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 10, get the equation:, then add the two sides of equation (12) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 57 Divide both sides of equation (3) by 10, get the equation:, then add the two sides of equation (13) to both sides of equation (2), get the equation:
Multiply both sides of equation (2) by 3 Divide both sides of equation (2) by 19, get the equation:, then add the two sides of equation (14) 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |