detailed information: The input equation set is:
| | | | 2 | A | + | | B | + | | 2 | C | + | | D | = | | | 369 5 | | (1) |
| | | | Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | A | + | | | 1 2 | B | + | | C | + | | | 1 2 | D | = | | | 369 10 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | 2 | A | + | | B | + | | 2 | C | + | | D | = | | | 369 5 | | (1) |
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Divide the two sides of equation (1) by 2, the equation can be obtained: | | A | + | | | 1 2 | B | + | | C | + | | | 1 2 | D | = | | | 369 10 | (6) | , then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
| | | | 2 | A | + | | B | + | | 2 | C | + | | D | = | | | 369 5 | | (1) |
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Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
| | | | 2 | A | + | | B | + | | 2 | C | + | | D | = | | | 369 5 | | (1) |
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Multiply both sides of equation (3) by 2, the equation can be obtained: , then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
| | | | 2 | A | + | | B | + | | 2 | C | + | | D | = | | | 369 5 | | (1) |
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由第(4)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》 |