detailed information: The input equation set is:
| | | | 5 | A | + | | | 5 2 | B | + | | | 15 8 | C | + | | | 63 40 | D | + | | | 63 40 | E | = | | | 343 40 | | (1) |
| | | 5 2 | A | + | | | 3 2 | B | + | | | 3 2 | C | + | | | 3 2 | D | + | | | 3 2 | E | = | | | 11 2 | | (2) |
| | | 3 2 | A | + | | | 3 2 | B | + | | | 3 2 | C | + | | | 3 2 | D | + | | | 3 2 | E | = | | | 9 2 | | (3) |
| | | 3 2 | A | + | | | 3 2 | B | + | | | 3 2 | C | + | | | 3 2 | D | + | | | 3 2 | E | = | | | 7 2 | | (4) |
| | | 3 2 | A | + | | | 3 2 | B | + | | | 3 2 | C | + | | | 3 2 | D | + | | | 3 2 | E | = | | | 7 2 | | (5) |
| Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | | 5 2 | A | + | | | 5 4 | B | + | | | 15 16 | C | + | | | 63 80 | D | + | | | 63 80 | E | = | | | 343 80 | (6) | , then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
| | | | 5 | A | + | | | 5 2 | B | + | | | 15 8 | C | + | | | 63 40 | D | + | | | 63 40 | E | = | | | 343 40 | | (1) |
| | | 1 4 | B | + | | | 9 16 | C | + | | | 57 80 | D | + | | | 57 80 | E | = | | | 97 80 | | (2) |
| | | 3 2 | A | + | | | 3 2 | B | + | | | 3 2 | C | + | | | 3 2 | D | + | | | 3 2 | E | = | | | 9 2 | | (3) |
| | | 3 2 | A | + | | | 3 2 | B | + | | | 3 2 | C | + | | | 3 2 | D | + | | | 3 2 | E | = | | | 7 2 | | (4) |
| | | 3 2 | A | + | | | 3 2 | B | + | | | 3 2 | C | + | | | 3 2 | D | + | | | 3 2 | E | = | | | 7 2 | | (5) |
|
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 10, the equation can be obtained: | | | 3 2 | A | + | | | 3 4 | B | + | | | 9 16 | C | + | | | 189 400 | D | + | | | 189 400 | E | = | | | 1029 400 | (7) | , then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
| | | | 5 | A | + | | | 5 2 | B | + | | | 15 8 | C | + | | | 63 40 | D | + | | | 63 40 | E | = | | | 343 40 | | (1) |
| | | 1 4 | B | + | | | 9 16 | C | + | | | 57 80 | D | + | | | 57 80 | E | = | | | 97 80 | | (2) |
| | | 3 4 | B | + | | | 15 16 | C | + | | | 411 400 | D | + | | | 411 400 | E | = | | | 771 400 | | (3) |
| | | 3 2 | A | + | | | 3 2 | B | + | | | 3 2 | C | + | | | 3 2 | D | + | | | 3 2 | E | = | | | 7 2 | | (4) |
| | | 3 2 | A | + | | | 3 2 | B | + | | | 3 2 | C | + | | | 3 2 | D | + | | | 3 2 | E | = | | | 7 2 | | (5) |
|
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 10, the equation can be obtained: | | | 3 2 | A | + | | | 3 4 | B | + | | | 9 16 | C | + | | | 189 400 | D | + | | | 189 400 | E | = | | | 1029 400 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | 5 | A | + | | | 5 2 | B | + | | | 15 8 | C | + | | | 63 40 | D | + | | | 63 40 | E | = | | | 343 40 | | (1) |
| | | 1 4 | B | + | | | 9 16 | C | + | | | 57 80 | D | + | | | 57 80 | E | = | | | 97 80 | | (2) |
| | | 3 4 | B | + | | | 15 16 | C | + | | | 411 400 | D | + | | | 411 400 | E | = | | | 771 400 | | (3) |
| | | 3 4 | B | + | | | 15 16 | C | + | | | 411 400 | D | + | | | 411 400 | E | = | | | 371 400 | | (4) |
| | | 3 2 | A | + | | | 3 2 | B | + | | | 3 2 | C | + | | | 3 2 | D | + | | | 3 2 | E | = | | | 7 2 | | (5) |
|
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 10, the equation can be obtained: | | | 3 2 | A | + | | | 3 4 | B | + | | | 9 16 | C | + | | | 189 400 | D | + | | | 189 400 | E | = | | | 1029 400 | (9) | , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
| | | | 5 | A | + | | | 5 2 | B | + | | | 15 8 | C | + | | | 63 40 | D | + | | | 63 40 | E | = | | | 343 40 | | (1) |
| | | 1 4 | B | + | | | 9 16 | C | + | | | 57 80 | D | + | | | 57 80 | E | = | | | 97 80 | | (2) |
| | | 3 4 | B | + | | | 15 16 | C | + | | | 411 400 | D | + | | | 411 400 | E | = | | | 771 400 | | (3) |
| | | 3 4 | B | + | | | 15 16 | C | + | | | 411 400 | D | + | | | 411 400 | E | = | | | 371 400 | | (4) |
| | | 3 4 | B | + | | | 15 16 | C | + | | | 411 400 | D | + | | | 411 400 | E | = | | | 371 400 | | (5) |
|
Multiply both sides of equation (2) by 3, the equation can be obtained: | | | 3 4 | B | + | | | 27 16 | C | + | | | 171 80 | D | + | | | 171 80 | E | = | | | 291 80 | (10) | , then subtract both sides of equation (10) from both sides of equation (3), the equations are reduced to:
| | | | 5 | A | + | | | 5 2 | B | + | | | 15 8 | C | + | | | 63 40 | D | + | | | 63 40 | E | = | | | 343 40 | | (1) |
| | | 1 4 | B | + | | | 9 16 | C | + | | | 57 80 | D | + | | | 57 80 | E | = | | | 97 80 | | (2) |
| - | 3 4 | C | | - | 111 100 | D | | - | 111 100 | E | = | | - | 171 100 | | (3) |
| | | 3 4 | B | + | | | 15 16 | C | + | | | 411 400 | D | + | | | 411 400 | E | = | | | 371 400 | | (4) |
| | | 3 4 | B | + | | | 15 16 | C | + | | | 411 400 | D | + | | | 411 400 | E | = | | | 371 400 | | (5) |
|
Multiply both sides of equation (2) by 3, the equation can be obtained: | | | 3 4 | B | + | | | 27 16 | C | + | | | 171 80 | D | + | | | 171 80 | E | = | | | 291 80 | (11) | , then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
| | | | 5 | A | + | | | 5 2 | B | + | | | 15 8 | C | + | | | 63 40 | D | + | | | 63 40 | E | = | | | 343 40 | | (1) |
| | | 1 4 | B | + | | | 9 16 | C | + | | | 57 80 | D | + | | | 57 80 | E | = | | | 97 80 | | (2) |
| - | 3 4 | C | | - | 111 100 | D | | - | 111 100 | E | = | | - | 171 100 | | (3) |
| - | 3 4 | C | | - | 111 100 | D | | - | 111 100 | E | = | | - | 271 100 | | (4) |
| | | 3 4 | B | + | | | 15 16 | C | + | | | 411 400 | D | + | | | 411 400 | E | = | | | 371 400 | | (5) |
|
Multiply both sides of equation (2) by 3, the equation can be obtained: | | | 3 4 | B | + | | | 27 16 | C | + | | | 171 80 | D | + | | | 171 80 | E | = | | | 291 80 | (12) | , then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
| | | | 5 | A | + | | | 5 2 | B | + | | | 15 8 | C | + | | | 63 40 | D | + | | | 63 40 | E | = | | | 343 40 | | (1) |
| | | 1 4 | B | + | | | 9 16 | C | + | | | 57 80 | D | + | | | 57 80 | E | = | | | 97 80 | | (2) |
| - | 3 4 | C | | - | 111 100 | D | | - | 111 100 | E | = | | - | 171 100 | | (3) |
| - | 3 4 | C | | - | 111 100 | D | | - | 111 100 | E | = | | - | 271 100 | | (4) |
| - | 3 4 | C | | - | 111 100 | D | | - | 111 100 | E | = | | - | 271 100 | | (5) |
|
Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
| | | | 5 | A | + | | | 5 2 | B | + | | | 15 8 | C | + | | | 63 40 | D | + | | | 63 40 | E | = | | | 343 40 | | (1) |
| | | 1 4 | B | + | | | 9 16 | C | + | | | 57 80 | D | + | | | 57 80 | E | = | | | 97 80 | | (2) |
| - | 3 4 | C | | - | 111 100 | D | | - | 111 100 | E | = | | - | 171 100 | | (3) |
| | - | 3 4 | C | | - | 111 100 | D | | - | 111 100 | E | = | | - | 271 100 | | (5) |
|
由第(4)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》 |