detailed information: The input equation set is:
| | | | | 4 25 | A | + | | | 57 10000 | C | | -1 | D | = | | | 40057 10000 | | (1) |
| | | 1 20 | A | + | | | 1 20 | C | | -1 | D | = | | | 121 20 | | (2) |
| | | 1 20 | A | + | | | 1 20 | B | + | | | 1 20 | C | | -1 | D | = | | | 161 20 | | (3) |
| | | 1 20 | A | + | | | 1 20 | B | + | | | 1 20 | C | | -1 | D | = | | | 201 20 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 16, the equation can be obtained: | | | 1 20 | A | + | | | 57 32000 | C | | - | 5 16 | D | = | | | 40057 32000 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | 4 25 | A | + | | | 57 10000 | C | | -1 | D | = | | | 40057 10000 | | (1) |
| | | 1543 32000 | C | | - | 11 16 | D | = | | | 153543 32000 | | (2) |
| | | 1 20 | A | + | | | 1 20 | B | + | | | 1 20 | C | | -1 | D | = | | | 161 20 | | (3) |
| | | 1 20 | A | + | | | 1 20 | B | + | | | 1 20 | C | | -1 | D | = | | | 201 20 | | (4) |
|
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 16, the equation can be obtained: | | | 1 20 | A | + | | | 57 32000 | C | | - | 5 16 | D | = | | | 40057 32000 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | 4 25 | A | + | | | 57 10000 | C | | -1 | D | = | | | 40057 10000 | | (1) |
| | | 1543 32000 | C | | - | 11 16 | D | = | | | 153543 32000 | | (2) |
| | | 1 20 | B | + | | | 1543 32000 | C | | - | 11 16 | D | = | | | 217543 32000 | | (3) |
| | | 1 20 | A | + | | | 1 20 | B | + | | | 1 20 | C | | -1 | D | = | | | 201 20 | | (4) |
|
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 16, the equation can be obtained: | | | 1 20 | A | + | | | 57 32000 | C | | - | 5 16 | D | = | | | 40057 32000 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | 4 25 | A | + | | | 57 10000 | C | | -1 | D | = | | | 40057 10000 | | (1) |
| | | 1543 32000 | C | | - | 11 16 | D | = | | | 153543 32000 | | (2) |
| | | 1 20 | B | + | | | 1543 32000 | C | | - | 11 16 | D | = | | | 217543 32000 | | (3) |
| | | 1 20 | B | + | | | 1543 32000 | C | | - | 11 16 | D | = | | | 281543 32000 | | (4) |
|
交After the exchange of equation (2) and equation (3), the equation system becomes:
| | | | | 4 25 | A | + | | | 57 10000 | C | | -1 | D | = | | | 40057 10000 | | (1) |
| | | 1 20 | B | + | | | 1543 32000 | C | | - | 11 16 | D | = | | | 217543 32000 | | (2) |
| | | 1543 32000 | C | | - | 11 16 | D | = | | | 153543 32000 | | (3) |
| | | 1 20 | B | + | | | 1543 32000 | C | | - | 11 16 | D | = | | | 281543 32000 | | (4) |
|
Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
| | | | | 4 25 | A | + | | | 57 10000 | C | | -1 | D | = | | | 40057 10000 | | (1) |
| | | 1 20 | B | + | | | 1543 32000 | C | | - | 11 16 | D | = | | | 217543 32000 | | (2) |
| | | 1543 32000 | C | | - | 11 16 | D | = | | | 153543 32000 | | (3) |
| |
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》 |