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 43, the equation can be obtained: | | 5 | x | | - | 25 43 | y | | - | 150 43 | z | = | | 0 | (4) | , then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
Multiply both sides of equation (1) by 7 Divide the two sides of equation (1) by 215, the equation can be obtained: | | | 7 5 | x | | - | 7 43 | y | | - | 42 43 | z | = | | 0 | (5) | , then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
Divide the two sides of equation (2) by 150, 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 (3) by 12075 Divide both sides of equation (3) by 43, 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 1125, 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 43 Divide both sides of equation (2) by 210, 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》 |