detailed information: The input equation set is:
| | | | | | 100 | A | + | | 4 | B | + | | 1024 | C | + | | 640 | D | = | | 784 | | (3) |
| | Question solving process:
Multiply both sides of equation (1) by 100, the equation can be obtained: , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | | -96 | B | + | | 1024 | C | + | | 640 | D | = | | 684 | | (3) |
| |
Multiply both sides of equation (1) by 4, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
| | | | | -96 | B | + | | 1024 | C | + | | 640 | D | = | | 684 | | (3) |
| |
Multiply both sides of equation (2) by 96 Divide the two sides of equation (2) by 7, the equation can be obtained: , then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
| | | | | | | 8704 7 | C | + | | 640 | D | = | | | 6324 7 | | (3) |
| |
Multiply both sides of equation (2) by 4 Divide the two sides of equation (2) by 7, the equation can be obtained: , then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
| | | | | | | 8704 7 | C | + | | 640 | D | = | | | 6324 7 | | (3) |
| |
Multiply both sides of equation (3) by 239 Divide the two sides of equation (3) by 8704, the equation can be obtained: | | | 239 7 | C | + | | | 1195 68 | D | = | | | 22227 896 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | | | | 8704 7 | C | + | | 640 | D | = | | | 6324 7 | | (3) |
| |
Multiply both sides of equation (4) by 8704 Divide both sides of equation (4) by 33, get the equation:, then subtract both sides of equation (10) from both sides of equation (3), get the equation:
| | | | | | | 8704 7 | C | = | | - | 1578688 231 | | (3) |
| |
Multiply both sides of equation (3) by 7 Divide both sides of equation (3) by 544, get the equation:, then subtract both sides of equation (11) from both sides of equation (2), get the equation:
| | | | | | | 8704 7 | C | = | | - | 1578688 231 | | (3) |
| |
Divide both sides of equation (2) by 7, get the equation:, then subtract both sides of equation (12) 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |