detailed information: The input equation set is:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | | | | Question solving process:
Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | | | |
Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | | | |
Divide the two sides of equation (2) by 2, the equation can be obtained: , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -2 | C | + | | D | | -2 | E | = | | - | 11009 2 | | (3) |
| | |
Divide the two sides of equation (2) by 2, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -2 | C | + | | D | | -2 | E | = | | - | 11009 2 | | (3) |
| | |
Divide the two sides of equation (2) by 2, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -2 | C | + | | D | | -2 | E | = | | - | 11009 2 | | (3) |
| | -1 | C | | -1 | D | | -2 | E | = | | - | 15587 2 | | (5) |
|
Divide the two sides of equation (3) by 2, the equation can be obtained: | -1 | C | + | | | 1 2 | D | | -1 | E | = | | - | 11009 4 | (9) | , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -2 | C | + | | D | | -2 | E | = | | - | 11009 2 | | (3) |
| | |
Multiply both sides of equation (4) by 3 Divide the two sides of equation (4) by 2, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | -2 | C | + | | D | | -2 | E | = | | - | 11009 2 | | (3) |
| | |
Multiply both sides of equation (5) by 2, get the equation:, then subtract both sides of equation (11) from both sides of equation (3), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | 2 | E | = | | 7974 | | (1) |
| | | | |
Multiply both sides of equation (5) by 2, get the equation:, then add the two sides of equation (12) to both sides of equation (1), get the equation:
Add both sides of equation (4) to both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 2, get the equation:, then add the two sides of equation (13) to both sides of equation (2), get the equation:
Add both sides of equation (3) to both sides of equation (1), get the equation:
Divide both sides of equation (2) by 2, get the equation:, then subtract both sides of equation (14) 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》 |