detailed information: The input equation set is:
| | | | | | 10 | x | + | | 10 | y | + | | 30 | z | = | | -10 | | (3) |
| Question solving process:
Divide the two sides of equation (1) by 4, the equation can be obtained: | | 5 | x | | - | 5 4 | y | + | | | 5 2 | z | = | | - | 5 4 | (4) | , then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
| | | | | | 10 | x | + | | 10 | y | + | | 30 | z | = | | -10 | | (3) |
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Divide the two sides of equation (1) by 2, the equation can be obtained: | | 10 | x | | - | 5 2 | y | + | | 5 | z | = | | - | 5 2 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 10 Divide the two sides of equation (2) by 19, 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 19 Divide both sides of equation (3) by 28, 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 19 Divide both sides of equation (3) by 35, 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 4 Divide both sides of equation (2) by 19, 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:
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》 |