detailed information: The input equation set is:
| | | | | 8 | A | + | | 4 | B | + | | 2 | C | + | | D | = | | 12 | | (2) |
| | 27 | A | + | | 9 | B | + | | 3 | C | + | | D | = | | 72 | | (3) |
| | Question solving process:
Multiply both sides of equation (1) by 8, the equation can be obtained: | | 8 | A | + | | 8 | B | + | | 8 | C | + | | 8 | D | = | | 0 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | | 27 | A | + | | 9 | B | + | | 3 | C | + | | D | = | | 72 | | (3) |
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Multiply both sides of equation (1) by 27, the equation can be obtained: | | 27 | A | + | | 27 | B | + | | 27 | C | + | | 27 | D | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 9 Divide the two sides of equation (2) by 2, the equation can be obtained: | -18 | B | | -27 | C | | - | 63 2 | D | = | | 54 | (7) | , then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (3) by 2, get the equation:, then add the two sides of equation (8) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 3, get the equation:, then subtract both sides of equation (9) from both sides of equation (1), get the equation:
Divide both sides of equation (2) by 4, get the equation:, then add the two sides of equation (10) 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:
Where: D are arbitrary constants. 解方程组的详细方法请参阅:《多元一次方程组的解法》 |