detailed information: The input equation set is: Question solving process:
Add both sides of equation (1) to both sides of equation (2) ,the equations are reduced to:
| | | | -3 | B | + | | 4 | C | | -20 | D | + | | 7 | E | = | | 0 | | (2) |
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Divide the two sides of equation (1) by 8, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (5), the equations are reduced to:
| | | | -3 | B | + | | 4 | C | | -20 | D | + | | 7 | E | = | | 0 | | (2) |
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Divide the two sides of equation (2) by 3, the equation can be obtained: | -1 | B | + | | | 4 3 | C | | - | 20 3 | D | + | | | 7 3 | E | = | | 0 | (7) | , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
| | | | -3 | B | + | | 4 | C | | -20 | D | + | | 7 | E | = | | 0 | | (2) |
| | | | 4 3 | C | | - | 20 3 | D | + | | | 10 3 | E | = | | 1 | | (4) |
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Divide the two sides of equation (2) by 8, the equation can be obtained: | - | 3 8 | B | + | | | 1 2 | C | | - | 5 2 | D | + | | | 7 8 | E | = | | 0 | (8) | , then add the two sides of equation (8) to both sides of equation (5), the equations are reduced to:
| | | | -3 | B | + | | 4 | C | | -20 | D | + | | 7 | E | = | | 0 | | (2) |
| | | | 4 3 | C | | - | 20 3 | D | + | | | 10 3 | E | = | | 1 | | (4) |
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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: , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | -3 | B | + | | 4 | C | | -20 | D | + | | 7 | E | = | | 0 | | (2) |
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Multiply both sides of equation (3) by 3 Divide the two sides of equation (3) by 2, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
| | | | -3 | B | + | | 4 | C | | -20 | D | + | | 7 | E | = | | 0 | | (2) |
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Divide the two sides of equation (4) by 2, the equation can be obtained: , then subtract both sides of equation (11) from both sides of equation (5), the equations are reduced to:
| | | | -3 | B | + | | 4 | C | | -20 | D | + | | 7 | E | = | | 0 | | (2) |
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Multiply both sides of equation (5) by 5 Divide both sides of equation (5) by 4, get the equation:, then add the two sides of equation (12) to both sides of equation (4), get the equation:
| | | | -3 | B | + | | 4 | C | | -20 | D | + | | 7 | E | = | | 0 | | (2) |
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Multiply both sides of equation (5) by 21 Divide both sides of equation (5) by 8, 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 (5) by 21 Divide both sides of equation (5) by 8, get the equation:, then add the two sides of equation (14) to both sides of equation (1), get the equation:
Divide both sides of equation (4) by 8, get the equation:, then add the two sides of equation (15) to both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (16) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 4, get the equation:, then subtract both sides of equation (17) from both sides of equation (2), get the equation:
Subtract both sides of equation (2) from 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》 |