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 2 | x | + | | | 25 86 | y | | - | 75 43 | z | = | | 0 | (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 14 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 75, the equation can be obtained: | | | 7 43 | y | + | | | 161 3225 | z | = | | | 14 75 | (6) | , 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 12075 Divide both sides of equation (3) by 86, get the equation:, then add the two sides of equation (7) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 1125 Divide both sides of equation (3) by 2, 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 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |