detailed information: The input equation set is:
| | | | - | 5 2 | x | + | | | 25 2 | y | | -2 | z | = | | 14 | | (2) |
| | Question solving process:
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 13, the equation can be obtained: | | | 5 2 | x | + | | | 25 26 | y | + | | | 75 13 | 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 14 Divide the two sides of equation (1) by 65, the equation can be obtained: | | | 7 5 | x | + | | | 7 13 | y | + | | | 42 13 | 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 25, 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 1225 Divide both sides of equation (3) by 1326, 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 125 Divide both sides of equation (3) by 34, 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 13 Divide both sides of equation (2) by 70, 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》 |