detailed information: The input equation set is:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | 8 | A | + | | 13 | B | + | | 15 | C | | -7 | D | | -12 | E | | -1 | F | = | | 1 | | (2) |
| | 9 | A | + | | 15 | B | + | | 18 | C | | -9 | D | | -15 | E | | -1 | F | = | | 1 | | (3) |
| -4 | A | | -7 | B | | -9 | C | + | | 5 | D | + | | 8 | E | + | | F | = | | 1 | | (4) |
| -7 | A | | -12 | B | | -15 | C | + | | 8 | D | + | | 13 | E | + | | F | = | | 1 | | (5) |
| | A | + | | B | + | | C | | -1 | D | | -1 | E | = | | 0 | | (6) |
| Question solving process:
Multiply both sides of equation (1) by 8 Divide the two sides of equation (1) by 5, the equation can be obtained: | | 8 | A | + | | | 64 5 | B | + | | | 72 5 | C | | - | 32 5 | D | | - | 56 5 | E | | - | 8 5 | F | = | | | 8 5 | (7) | , then subtract both sides of equation (7) from both sides of equation (2), the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | 9 | A | + | | 15 | B | + | | 18 | C | | -9 | D | | -15 | E | | -1 | F | = | | 1 | | (3) |
| -4 | A | | -7 | B | | -9 | C | + | | 5 | D | + | | 8 | E | + | | F | = | | 1 | | (4) |
| -7 | A | | -12 | B | | -15 | C | + | | 8 | D | + | | 13 | E | + | | F | = | | 1 | | (5) |
| | A | + | | B | + | | C | | -1 | D | | -1 | E | = | | 0 | | (6) |
|
Multiply both sides of equation (1) by 9 Divide the two sides of equation (1) by 5, the equation can be obtained: | | 9 | A | + | | | 72 5 | B | + | | | 81 5 | C | | - | 36 5 | D | | - | 63 5 | E | | - | 9 5 | F | = | | | 9 5 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | | 3 5 | B | + | | | 9 5 | C | | - | 9 5 | D | | - | 12 5 | E | + | | | 4 5 | F | = | | - | 4 5 | | (3) |
| -4 | A | | -7 | B | | -9 | C | + | | 5 | D | + | | 8 | E | + | | F | = | | 1 | | (4) |
| -7 | A | | -12 | B | | -15 | C | + | | 8 | D | + | | 13 | E | + | | F | = | | 1 | | (5) |
| | A | + | | B | + | | C | | -1 | D | | -1 | E | = | | 0 | | (6) |
|
Multiply both sides of equation (1) by 4 Divide the two sides of equation (1) by 5, the equation can be obtained: | | 4 | A | + | | | 32 5 | B | + | | | 36 5 | C | | - | 16 5 | D | | - | 28 5 | E | | - | 4 5 | F | = | | | 4 5 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | | 3 5 | B | + | | | 9 5 | C | | - | 9 5 | D | | - | 12 5 | E | + | | | 4 5 | F | = | | - | 4 5 | | (3) |
| - | 3 5 | B | | - | 9 5 | C | + | | | 9 5 | D | + | | | 12 5 | E | + | | | 1 5 | F | = | | | 9 5 | | (4) |
| -7 | A | | -12 | B | | -15 | C | + | | 8 | D | + | | 13 | E | + | | F | = | | 1 | | (5) |
| | A | + | | B | + | | C | | -1 | D | | -1 | E | = | | 0 | | (6) |
|
Multiply both sides of equation (1) by 7 Divide the two sides of equation (1) by 5, the equation can be obtained: | | 7 | A | + | | | 56 5 | B | + | | | 63 5 | C | | - | 28 5 | D | | - | 49 5 | E | | - | 7 5 | F | = | | | 7 5 | (10) | , then add the two sides of equation (10) to both sides of equation (5), the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | | 3 5 | B | + | | | 9 5 | C | | - | 9 5 | D | | - | 12 5 | E | + | | | 4 5 | F | = | | - | 4 5 | | (3) |
| - | 3 5 | B | | - | 9 5 | C | + | | | 9 5 | D | + | | | 12 5 | E | + | | | 1 5 | F | = | | | 9 5 | | (4) |
| - | 4 5 | B | | - | 12 5 | C | + | | | 12 5 | D | + | | | 16 5 | E | | - | 2 5 | F | = | | | 12 5 | | (5) |
| | A | + | | B | + | | C | | -1 | D | | -1 | E | = | | 0 | | (6) |
|
Divide the two sides of equation (1) by 5, the equation can be obtained: | | A | + | | | 8 5 | B | + | | | 9 5 | C | | - | 4 5 | D | | - | 7 5 | E | | - | 1 5 | F | = | | | 1 5 | (11) | , then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | | 3 5 | B | + | | | 9 5 | C | | - | 9 5 | D | | - | 12 5 | E | + | | | 4 5 | F | = | | - | 4 5 | | (3) |
| - | 3 5 | B | | - | 9 5 | C | + | | | 9 5 | D | + | | | 12 5 | E | + | | | 1 5 | F | = | | | 9 5 | | (4) |
| - | 4 5 | B | | - | 12 5 | C | + | | | 12 5 | D | + | | | 16 5 | E | | - | 2 5 | F | = | | | 12 5 | | (5) |
| - | 3 5 | B | | - | 4 5 | C | | - | 1 5 | D | + | | | 2 5 | E | + | | | 1 5 | F | = | | - | 1 5 | | (6) |
|
Multiply both sides of equation (2) by 3, the equation can be obtained: | | | 3 5 | B | + | | | 9 5 | C | | - | 9 5 | D | | - | 12 5 | E | + | | | 9 5 | F | = | | - | 9 5 | (12) | , then subtract both sides of equation (12) from both sides of equation (3), the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | - | 3 5 | B | | - | 9 5 | C | + | | | 9 5 | D | + | | | 12 5 | E | + | | | 1 5 | F | = | | | 9 5 | | (4) |
| - | 4 5 | B | | - | 12 5 | C | + | | | 12 5 | D | + | | | 16 5 | E | | - | 2 5 | F | = | | | 12 5 | | (5) |
| - | 3 5 | B | | - | 4 5 | C | | - | 1 5 | D | + | | | 2 5 | E | + | | | 1 5 | F | = | | - | 1 5 | | (6) |
|
Multiply both sides of equation (2) by 3, the equation can be obtained: | | | 3 5 | B | + | | | 9 5 | C | | - | 9 5 | D | | - | 12 5 | E | + | | | 9 5 | F | = | | - | 9 5 | (13) | , then add the two sides of equation (13) to both sides of equation (4), the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | | - | 4 5 | B | | - | 12 5 | C | + | | | 12 5 | D | + | | | 16 5 | E | | - | 2 5 | F | = | | | 12 5 | | (5) |
| - | 3 5 | B | | - | 4 5 | C | | - | 1 5 | D | + | | | 2 5 | E | + | | | 1 5 | F | = | | - | 1 5 | | (6) |
|
Multiply both sides of equation (2) by 4, the equation can be obtained: | | | 4 5 | B | + | | | 12 5 | C | | - | 12 5 | D | | - | 16 5 | E | + | | | 12 5 | F | = | | - | 12 5 | (14) | , then add the two sides of equation (14) to both sides of equation (5), the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | | | - | 3 5 | B | | - | 4 5 | C | | - | 1 5 | D | + | | | 2 5 | E | + | | | 1 5 | F | = | | - | 1 5 | | (6) |
|
Multiply both sides of equation (2) by 3, the equation can be obtained: | | | 3 5 | B | + | | | 9 5 | C | | - | 9 5 | D | | - | 12 5 | E | + | | | 9 5 | F | = | | - | 9 5 | (15) | , then add the two sides of equation (15) to both sides of equation (6), the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | | | |
交After the exchange of equation (3) and equation (6), the equation system becomes:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | | | |
Subtract both sides of equation (4) from both sides of equation (5) ,the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | | | |
Divide the two sides of equation (4) by 2, the equation can be obtained: , then add the two sides of equation (16) to both sides of equation (6), the equations are reduced to:
| | | | 5 | A | + | | 8 | B | + | | 9 | C | | -4 | D | | -7 | E | | -1 | F | = | | 1 | | (1) |
| | | 1 5 | B | + | | | 3 5 | C | | - | 3 5 | D | | - | 4 5 | E | + | | | 3 5 | F | = | | - | 3 5 | | (2) |
| | | | |
由第(6)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》 |