detailed information: The input equation set is:
| | | | 1000 | x | + | | 1000 | y | + | | 1000 | z | = | | 9 | | (1) |
| | 500 | x | + | | 500 | y | + | | 1000 | z | = | | 6 | | (2) |
| | 300 | x | + | | 100 | y | + | | 100 | z | = | | 2 | | (3) |
| Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | 500 | x | + | | 500 | y | + | | 500 | z | = | | | 9 2 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | 1000 | x | + | | 1000 | y | + | | 1000 | z | = | | 9 | | (1) |
| | | 300 | x | + | | 100 | y | + | | 100 | z | = | | 2 | | (3) |
|
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 10, the equation can be obtained: | | 300 | x | + | | 300 | y | + | | 300 | z | = | | | 27 10 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | 1000 | x | + | | 1000 | y | + | | 1000 | z | = | | 9 | | (1) |
| | |
交After the exchange of equation (2) and equation (3), the equation system becomes:
| | | | 1000 | x | + | | 1000 | y | + | | 1000 | z | = | | 9 | | (1) |
| | |
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 5, get the equation:, then add the two sides of equation (6) to both sides of equation (2), get the equation:
| | | | 1000 | x | + | | 1000 | y | + | | 1000 | z | = | | 9 | | (1) |
| | |
Multiply both sides of equation (3) by 2, get the equation:, then subtract both sides of equation (7) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 5, get the equation:, then add the two sides of equation (8) 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》 |