detailed information: The input equation set is:
| | | | 80 | A | | -40 | B | | -40 | C | + | | D | = | | 0 | | (1) |
| | | | Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | 40 | A | | -20 | B | | -20 | C | + | | | 1 2 | D | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
| | | | 80 | A | | -40 | B | | -40 | C | + | | D | = | | 0 | | (1) |
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Divide the two sides of equation (1) by 2, the equation can be obtained: | | 40 | A | | -20 | B | | -20 | C | + | | | 1 2 | D | = | | 0 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | | 80 | A | | -40 | B | | -40 | C | + | | D | = | | 0 | | (1) |
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Divide the two sides of equation (1) by 80, the equation can be obtained: | | A | | - | 1 2 | B | | - | 1 2 | C | + | | | 1 80 | D | = | | 0 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | 80 | A | | -40 | B | | -40 | C | + | | D | = | | 0 | | (1) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | | 80 | A | | -40 | B | | -40 | C | + | | D | = | | 0 | | (1) |
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Divide the two sides of equation (2) by 80, the equation can be obtained: | | | 1 2 | B | | - | 1 4 | C | + | | | 1 160 | D | = | | - | 3 40 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | 80 | A | | -40 | B | | -40 | C | + | | D | = | | 0 | | (1) |
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Divide the two sides of equation (3) by 40, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | 80 | A | | -40 | B | | -40 | C | + | | D | = | | 0 | | (1) |
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Multiply both sides of equation (4) by 20, get the equation:, then add the two sides of equation (11) to both sides of equation (3), get the equation:
| | | | 80 | A | | -40 | B | | -40 | C | + | | D | = | | 0 | | (1) |
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Multiply both sides of equation (4) by 40 Divide both sides of equation (4) by 3, get the equation:, then add the two sides of equation (12) to both sides of equation (2), get the equation:
| | | | 80 | A | | -40 | B | | -40 | C | + | | D | = | | 0 | | (1) |
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Multiply both sides of equation (4) by 80 Divide both sides of equation (4) by 3, get the equation:, then add the two sides of equation (13) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 3, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 4 Divide both sides of equation (3) by 3, get the equation:, then add the two sides of equation (15) to both sides of equation (1), 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》 |