detailed information: The input equation set is:
| | | | | | 4 | A | + | | 30 | B | | -20 | C | + | | 7 | D | = | | 10 | | (3) |
| | Question solving process:
Multiply both sides of equation (1) by 2, the equation can be obtained: | | 2 | A | | -12 | B | + | | 8 | C | | -10 | D | = | | 2 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | | 4 | A | + | | 30 | B | | -20 | C | + | | 7 | D | = | | 10 | | (3) |
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Multiply both sides of equation (1) by 4, the equation can be obtained: | | 4 | A | | -24 | B | + | | 16 | C | | -20 | D | = | | 4 | (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 3, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
Divide both sides of equation (2) by 3, get the equation:, then add the two sides of equation (8) 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:
Where: C, 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》 |