detailed information: The input equation set is:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | | | | Question solving process:
Multiply both sides of equation (1) by 2, the equation can be obtained: | | 2 | A | + | | 2 | B | + | | 4 | C | + | | 4 | E | = | | 15948 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
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Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
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Add both sides of equation (2) to both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -4 | C | + | | 2 | D | | -4 | E | = | | -12850 | | (3) |
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Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -4 | C | + | | 2 | D | | -4 | E | = | | -12850 | | (3) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -4 | C | + | | 2 | D | | -4 | E | = | | -12850 | | (3) |
| | -1 | C | | -1 | D | | -2 | E | = | | - | 15587 2 | | (5) |
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Divide the two sides of equation (3) by 4, the equation can be obtained: | -1 | C | + | | | 1 2 | D | | -1 | E | = | | - | 6425 2 | (8) | , then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -4 | C | + | | 2 | D | | -4 | E | = | | -12850 | | (3) |
| | -1 | C | | -1 | D | | -2 | E | = | | - | 15587 2 | | (5) |
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Divide the two sides of equation (3) by 4, the equation can be obtained: | -1 | C | + | | | 1 2 | D | | -1 | E | = | | - | 6425 2 | (9) | , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -4 | C | + | | 2 | D | | -4 | E | = | | -12850 | | (3) |
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Subtract both sides of equation (4) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -4 | C | + | | 2 | D | | -4 | E | = | | -12850 | | (3) |
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由第(5)方程式可以看出,该方程组无解。
解方程组的详细方法请参阅:《多元一次方程组的解法》 |