detailed information: The input equation set is: Question solving process:
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 2, the equation can be obtained: | | 5 | x | + | | 10 | y | + | | | 15 2 | z | = | | | 75 2 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
Multiply both sides of equation (1) by 2, 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 9 Divide the two sides of equation (2) by 16, the equation can be obtained: | -9 | y | | - | 243 32 | z | = | | - | 1593 32 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (3) by 432 Divide both sides of equation (3) by 115, 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 96 Divide both sides of equation (3) by 115, get the equation:, then add the two sides of equation (8) to both sides of equation (1), get the equation:
Divide both sides of equation (2) by 4, 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |