detailed information: The input equation set is:
| | | | -32 | A | + | | 8 | B | + | | 32 | C | | -1 | D | = | | 20 | | (2) |
| -8 | A | + | | 40 | B | + | | 8 | C | | -1 | D | = | | 0 | | (3) |
| | Question solving process:
Multiply both sides of equation (1) by 32, the equation can be obtained: , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
| | | | | -8 | A | + | | 40 | B | + | | 8 | C | | -1 | D | = | | 0 | | (3) |
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Multiply both sides of equation (1) by 8, the equation can be obtained: , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 5, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 13 Divide the two sides of equation (2) by 40, the equation can be obtained: | | | 13 5 | B | + | | | 52 5 | C | | - | 13 40 | D | = | | | 403 50 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | | | - | 47 5 | C | + | | | 13 40 | D | = | | - | 403 50 | | (4) |
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Multiply both sides of equation (3) by 47 Divide the two sides of equation (3) by 760, the equation can be obtained: | - | 47 5 | C | + | | | 47 190 | D | = | | - | 14429 1900 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (4) by 3040 Divide both sides of equation (4) by 59, get the equation:, then subtract both sides of equation (10) from both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 760 Divide both sides of equation (4) by 59, get the equation:, then add the two sides of equation (11) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 4 Divide both sides of equation (3) by 19, get the equation:, then add the two sides of equation (12) to both sides of equation (2), 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |