detailed information: The input equation set is:
| | | | | | 3 10 | A | | - | 7 10 | B | + | | | 2 5 | C | = | | 0 | | (2) |
| | | 2 5 | A | + | | | 2 5 | B | | - | 2 5 | C | + | | | 2 5 | D | = | | 0 | | (3) |
| | | 2 5 | B | + | | | 2 5 | C | | - | 2 5 | D | + | | | 2 5 | E | = | | 0 | | (4) |
| | | 2 5 | C | + | | | 2 5 | D | | - | 2 5 | E | + | | | 2 5 | F | = | | 0 | | (5) |
| | | 2 5 | D | + | | | 2 5 | E | | - | 2 5 | F | + | | | 2 5 | G | = | | 0 | | (6) |
| | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | = | | 1 | | (8) |
| Question solving process:
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 4, the equation can be obtained: , then add the two sides of equation (9) to both sides of equation (2), the equations are reduced to:
| | | | | | | 2 5 | A | + | | | 2 5 | B | | - | 2 5 | C | + | | | 2 5 | D | = | | 0 | | (3) |
| | | 2 5 | B | + | | | 2 5 | C | | - | 2 5 | D | + | | | 2 5 | E | = | | 0 | | (4) |
| | | 2 5 | C | + | | | 2 5 | D | | - | 2 5 | E | + | | | 2 5 | F | = | | 0 | | (5) |
| | | 2 5 | D | + | | | 2 5 | E | | - | 2 5 | F | + | | | 2 5 | G | = | | 0 | | (6) |
| | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | = | | 1 | | (8) |
|
Add both sides of equation (1) to both sides of equation (3) ,the equations are reduced to:
| | | | | | | | 2 5 | B | + | | | 2 5 | C | | - | 2 5 | D | + | | | 2 5 | E | = | | 0 | | (4) |
| | | 2 5 | C | + | | | 2 5 | D | | - | 2 5 | E | + | | | 2 5 | F | = | | 0 | | (5) |
| | | 2 5 | D | + | | | 2 5 | E | | - | 2 5 | F | + | | | 2 5 | G | = | | 0 | | (6) |
| | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | = | | 1 | | (8) |
|
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 2, the equation can be obtained: , then add the two sides of equation (10) to both sides of equation (8), the equations are reduced to:
| | | | | | | | 2 5 | B | + | | | 2 5 | C | | - | 2 5 | D | + | | | 2 5 | E | = | | 0 | | (4) |
| | | 2 5 | C | + | | | 2 5 | D | | - | 2 5 | E | + | | | 2 5 | F | = | | 0 | | (5) |
| | | 2 5 | D | + | | | 2 5 | E | | - | 2 5 | F | + | | | 2 5 | G | = | | 0 | | (6) |
| | | 2 | B | + | | C | + | | D | + | | E | + | | F | + | | G | = | | 1 | | (8) |
|
Multiply both sides of equation (2) by 2, the equation can be obtained: , then add the two sides of equation (11) to both sides of equation (3), the equations are reduced to:
| | | | | | | | 2 5 | B | + | | | 2 5 | C | | - | 2 5 | D | + | | | 2 5 | E | = | | 0 | | (4) |
| | | 2 5 | C | + | | | 2 5 | D | | - | 2 5 | E | + | | | 2 5 | F | = | | 0 | | (5) |
| | | 2 5 | D | + | | | 2 5 | E | | - | 2 5 | F | + | | | 2 5 | G | = | | 0 | | (6) |
| | | 2 | B | + | | C | + | | D | + | | E | + | | F | + | | G | = | | 1 | | (8) |
|
Add both sides of equation (2) to both sides of equation (4) ,the equations are reduced to:
| | | | | | | | | 2 5 | C | + | | | 2 5 | D | | - | 2 5 | E | + | | | 2 5 | F | = | | 0 | | (5) |
| | | 2 5 | D | + | | | 2 5 | E | | - | 2 5 | F | + | | | 2 5 | G | = | | 0 | | (6) |
| | | 2 | B | + | | C | + | | D | + | | E | + | | F | + | | G | = | | 1 | | (8) |
|
Multiply both sides of equation (2) by 5, the equation can be obtained: , then add the two sides of equation (12) to both sides of equation (8), the equations are reduced to:
| | | | | | | | | 2 5 | C | + | | | 2 5 | D | | - | 2 5 | E | + | | | 2 5 | F | = | | 0 | | (5) |
| | | 2 5 | D | + | | | 2 5 | E | | - | 2 5 | F | + | | | 2 5 | G | = | | 0 | | (6) |
| | | 3 | C | + | | D | + | | E | + | | F | + | | G | = | | 1 | | (8) |
|
Multiply both sides of equation (3) by 2, the equation can be obtained: , then subtract both sides of equation (13) from both sides of equation (4), the equations are reduced to:
| | | | | | | | | 2 5 | C | + | | | 2 5 | D | | - | 2 5 | E | + | | | 2 5 | F | = | | 0 | | (5) |
| | | 2 5 | D | + | | | 2 5 | E | | - | 2 5 | F | + | | | 2 5 | G | = | | 0 | | (6) |
| | | 3 | C | + | | D | + | | E | + | | F | + | | G | = | | 1 | | (8) |
|
Subtract both sides of equation (3) from both sides of equation (5) ,the equations are reduced to:
| | | | | | | | | | 2 5 | D | + | | | 2 5 | E | | - | 2 5 | F | + | | | 2 5 | G | = | | 0 | | (6) |
| | | 3 | C | + | | D | + | | E | + | | F | + | | G | = | | 1 | | (8) |
|
Multiply both sides of equation (3) by 15 Divide the two sides of equation (3) by 2, the equation can be obtained: , then subtract both sides of equation (14) from both sides of equation (8), the equations are reduced to:
| | | | | | | | | | 2 5 | D | + | | | 2 5 | E | | - | 2 5 | F | + | | | 2 5 | G | = | | 0 | | (6) |
| | |
Divide the two sides of equation (4) by 3, the equation can be obtained: , then add the two sides of equation (15) to both sides of equation (6), the equations are reduced to:
Multiply both sides of equation (4) by 5 Divide the two sides of equation (4) by 3, the equation can be obtained: , then subtract both sides of equation (16) from both sides of equation (8), the equations are reduced to:
Multiply both sides of equation (5) by 4 Divide the two sides of equation (5) by 3, the equation can be obtained: , then add the two sides of equation (17) to both sides of equation (6), the equations are reduced to:
Add both sides of equation (5) to both sides of equation (7) ,the equations are reduced to:
Multiply both sides of equation (5) by 5 Divide the two sides of equation (5) by 6, the equation can be obtained: , then add the two sides of equation (18) to both sides of equation (8), the equations are reduced to:
Multiply both sides of equation (6) by 6, the equation can be obtained: , then subtract both sides of equation (19) from both sides of equation (7), the equations are reduced to:
Multiply both sides of equation (6) by 10, the equation can be obtained: , then subtract both sides of equation (20) from both sides of equation (8), the equations are reduced to:
Multiply both sides of equation (7) by 15 Divide the two sides of equation (7) by 14, the equation can be obtained: , then subtract both sides of equation (21) from both sides of equation (8), the equations are reduced to:
由第(8)方程式可以看出,该方程组无解。
解方程组的详细方法请参阅:《多元一次方程组的解法》 |