detailed information: The input equation set is: Question solving process:
Divide the two sides of equation (1) by 3, the equation can be obtained: , then add the two sides of equation (6) to both sides of equation (2), the equations are reduced to:
Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 3, the equation can be obtained: , then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
 | | | | | - | 2 3 | B | + | | | 11 3 | C | | -4 | D | = | | -9 | | (3) |
| | |
Divide the two sides of equation (1) by 3, the equation can be obtained: , then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 | | | | | - | 2 3 | B | + | | | 11 3 | C | | -4 | D | = | | -9 | | (3) |
| | |
Divide the two sides of equation (1) by 3, the equation can be obtained: , then add the two sides of equation (9) to both sides of equation (5), the equations are reduced to:
 | | | | | - | 2 3 | B | + | | | 11 3 | C | | -4 | D | = | | -9 | | (3) |
| | |
Multiply both sides of equation (2) by 2 Divide the two sides of equation (2) by 5, the equation can be obtained: | | | 2 3 | B | | - | 4 15 | C | + | | | 8 5 | D | = | | 0 | (10) | , then add the two sides of equation (10) to both sides of equation (3), the equations are reduced to:
Divide the two sides of equation (2) by 5, the equation can be obtained: | | | 1 3 | B | | - | 2 15 | C | + | | | 4 5 | D | = | | 0 | (11) | , then add the two sides of equation (11) to both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (2) by 2 Divide the two sides of equation (2) by 5, the equation can be obtained: | | | 2 3 | B | | - | 4 15 | C | + | | | 8 5 | D | = | | 0 | (12) | , then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
Divide the two sides of equation (3) by 17, the equation can be obtained: , then subtract both sides of equation (13) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (3) by 2 Divide the two sides of equation (3) by 17, the equation can be obtained: | | | 2 5 | C | | - | 24 85 | D | = | | - | 18 17 | (14) | , then add the two sides of equation (14) to both sides of equation (5), the equations are reduced to:
Multiply both sides of equation (4) by 32, the equation can be obtained: , then subtract both sides of equation (15) from both sides of equation (5), the equations are reduced to:
Multiply both sides of equation (4) by 204 Divide both sides of equation (4) by 5, get the equation:, then subtract both sides of equation (16) from both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 68, get the equation:, then add the two sides of equation (17) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 10 Divide both sides of equation (3) by 51, get the equation:, then add the two sides of equation (18) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 10 Divide both sides of equation (3) by 17, get the equation:, then add the two sides of equation (19) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 3 Divide both sides of equation (2) by 5, get the equation:, then add the two sides of equation (20) 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |