detailed information: The input equation set is:
| | | | | 75 | x | + | | 50 | y | + | | 25 | z | = | | 100 | | (2) |
| | Question solving process:
Multiply both sides of equation (1) by 15 Divide the two sides of equation (1) by 2, the equation can be obtained: | -75 | x | + | | | 75 2 | y | | - | 75 4 | z | = | | | 75 8 | (4) | , then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
Divide the two sides of equation (1) by 10, the equation can be obtained: , then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 3 Divide the two sides of equation (2) by 175, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (3) by 175 Divide both sides of equation (3) by 18, get the equation:, then subtract both sides of equation (7) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 35 Divide both sides of equation (3) by 9, get the equation:, then add the two sides of equation (8) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 2 Divide both sides of equation (2) by 35, get the equation:, then subtract both sides of equation (9) 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》 |