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: | | 4 | A | | - | 8 3 | B | | - | 4 3 | C | = | | - | 16 3 | (6) | , then add the two sides of equation (6) to both sides of equation (2), the equations are reduced to:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
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Divide the two sides of equation (1) by 3, the equation can be obtained: | | 2 | A | | - | 4 3 | B | | - | 2 3 | C | = | | - | 8 3 | (7) | , then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
| - | 4 3 | B | + | | | 13 3 | C | + | | D | = | | | 22 3 | | (3) |
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Divide the two sides of equation (1) by 6, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
| - | 4 3 | B | + | | | 13 3 | C | + | | D | = | | | 22 3 | | (3) |
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Multiply both sides of equation (2) by 2 Divide the two sides of equation (2) by 5, the equation can be obtained: | | | 4 3 | B | | - | 8 15 | C | | - | 2 5 | D | = | | - | 14 15 | (9) | , then add the two sides of equation (9) to both sides of equation (3), the equations are reduced to:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
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Divide the two sides of equation (2) by 5, the equation can be obtained: | | | 2 3 | B | | - | 4 15 | C | | - | 1 5 | D | = | | - | 7 15 | (10) | , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
| | - | 2 5 | C | + | | | 1 5 | D | + | | | 1 2 | E | = | | | 9 5 | | (4) |
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Multiply both sides of equation (2) by 3 Divide the two sides of equation (2) by 10, the equation can be obtained: | | B | | - | 2 5 | C | | - | 3 10 | D | = | | - | 7 10 | (11) | , then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
| | - | 2 5 | C | + | | | 1 5 | D | + | | | 1 2 | E | = | | | 9 5 | | (4) |
| | | 3 5 | C | | - | 3 10 | D | + | | | 1 4 | E | = | | - | 7 10 | | (5) |
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Multiply both sides of equation (3) by 2 Divide the two sides of equation (3) by 19, the equation can be obtained: , then add the two sides of equation (12) to both sides of equation (4), the equations are reduced to:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
| | | | | 3 5 | C | | - | 3 10 | D | + | | | 1 4 | E | = | | - | 7 10 | | (5) |
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Multiply both sides of equation (3) by 3 Divide the two sides of equation (3) by 19, the equation can be obtained: , then subtract both sides of equation (13) from both sides of equation (5), the equations are reduced to:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
| | | - | 15 38 | D | + | | | 1 4 | E | = | | - | 65 38 | | (5) |
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Multiply both sides of equation (4) by 3 Divide the two sides of equation (4) by 2, the equation can be obtained: , then add the two sides of equation (14) to both sides of equation (5), the equations are reduced to:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
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Divide both sides of equation (5) by 2, get the equation:, then subtract both sides of equation (15) from both sides of equation (4), get the equation:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
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Multiply both sides of equation (4) by 57 Divide both sides of equation (4) by 25, get the equation:, then subtract both sides of equation (16) from both sides of equation (3), get the equation:
| | | | | | 10 3 | B | | - | 4 3 | C | | -1 | D | = | | - | 7 3 | | (2) |
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Multiply both sides of equation (4) by 19 Divide both sides of equation (4) by 5, 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 (3) by 20 Divide both sides of equation (3) by 57, 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 10 Divide both sides of equation (3) by 19, 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 6 Divide both sides of equation (2) by 5, 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》 |