detailed information: The input equation set is:
| | | | 800 | A | + | | 2 | B | + | | 10 | C | + | | D | = | | 30 | | (1) |
| | 400 | A | + | | 2 | B | + | | 10 | C | + | | D | = | | 6 | | (2) |
| | 800 | A | + | | 10 | B | + | | 10 | C | + | | D | = | | 30 | | (3) |
| | 800 | A | + | | 2 | B | + | | 2 | C | + | | D | = | | 38 | | (4) |
| Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | 400 | A | + | | B | + | | 5 | C | + | | | 1 2 | D | = | | 15 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | 800 | A | + | | 2 | B | + | | 10 | C | + | | D | = | | 30 | | (1) |
| | | 800 | A | + | | 10 | B | + | | 10 | C | + | | D | = | | 30 | | (3) |
| | 800 | A | + | | 2 | B | + | | 2 | C | + | | D | = | | 38 | | (4) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | 800 | A | + | | 2 | B | + | | 10 | C | + | | D | = | | 30 | | (1) |
| | | | 800 | A | + | | 2 | B | + | | 2 | C | + | | D | = | | 38 | | (4) |
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Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
| | | | 800 | A | + | | 2 | B | + | | 10 | C | + | | D | = | | 30 | | (1) |
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Multiply both sides of equation (2) by 8, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | 800 | A | + | | 2 | B | + | | 10 | C | + | | D | = | | 30 | | (1) |
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Divide the two sides of equation (3) by 5, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | 800 | A | + | | 2 | B | + | | 10 | C | + | | D | = | | 30 | | (1) |
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Multiply both sides of equation (4) by 5, get the equation:, then add the two sides of equation (8) to both sides of equation (3), get the equation:
| | | | 800 | A | + | | 2 | B | + | | 10 | C | + | | D | = | | 30 | | (1) |
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Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 8, get the equation:, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
| | | | 800 | A | + | | 2 | B | + | | 10 | C | + | | D | = | | 30 | | (1) |
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Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 4, get the equation:, then subtract both sides of equation (10) from both sides of equation (1), get the equation:
Divide both sides of equation (3) by 8, get the equation:, then add the two sides of equation (11) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 4, 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 (2) by 2, get the equation:, then subtract both sides of equation (13) 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》 |