detailed information: The input equation set is:
| | | | 8 | A | + | | 4 | B | + | | 2 | C | + | | D | = | | 100 | | (1) |
| | | 4 | A | + | | 3 | B | + | | C | + | | D | = | | | 157 2 | | (3) |
| | Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | 4 | A | + | | 2 | B | + | | C | + | | | 1 2 | D | = | | 50 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | 8 | A | + | | 4 | B | + | | 2 | C | + | | D | = | | 100 | | (1) |
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交After the exchange of equation (2) and equation (3), the equation system becomes:
| | | | 8 | A | + | | 4 | B | + | | 2 | C | + | | D | = | | 100 | | (1) |
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Subtract both sides of equation (3) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 4, get the equation:, then subtract both sides of equation (6) 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:
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》 |