detailed information: The input equation set is:
| | | | 6 | x | + | | 244 | y | + | | 1525 | z | = | | 7 | | (1) |
| | 8 | x | + | | 244 | y | + | | 2071 | z | = | | 11 | | (2) |
| | 10 | x | + | | 244 | y | + | | 2637 | z | = | | 15 | | (3) |
| Question solving process:
Multiply both sides of equation (1) by 4 Divide the two sides of equation (1) by 3, the equation can be obtained: | | 8 | x | + | | | 976 3 | y | + | | | 6100 3 | z | = | | | 28 3 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | 6 | x | + | | 244 | y | + | | 1525 | z | = | | 7 | | (1) |
| | | 10 | x | + | | 244 | y | + | | 2637 | z | = | | 15 | | (3) |
|
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 3, the equation can be obtained: | | 10 | x | + | | | 1220 3 | y | + | | | 7625 3 | z | = | | | 35 3 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | 6 | x | + | | 244 | y | + | | 1525 | z | = | | 7 | | (1) |
| | - | 488 3 | y | + | | | 286 3 | z | = | | | 10 3 | | (3) |
|
Multiply both sides of equation (2) by 2, the equation can be obtained: | - | 488 3 | y | + | | | 226 3 | z | = | | | 10 3 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | 6 | x | + | | 244 | y | + | | 1525 | z | = | | 7 | | (1) |
| | |
Multiply both sides of equation (3) by 113 Divide both sides of equation (3) by 60, get the equation:, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
| | | | 6 | x | + | | 244 | y | + | | 1525 | z | = | | 7 | | (1) |
| | |
Multiply both sides of equation (3) by 305 Divide both sides of equation (3) by 4, get the equation:, then subtract both sides of equation (8) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 3, get the equation:, then add the two sides of equation (9) 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |