detailed information: The input equation set is:
| | | | | | 1 2 | A | + | | | 21 20 | B | + | | | 109 100 | C | + | | | 9 100 | D | = | | 0 | | (2) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | + | | | 209 100 | D | = | | 0 | | (3) |
| | | 109 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | - | 9 100 | D | = | | 0 | | (4) |
| Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | | 1 2 | A | + | | | 1 2 | B | + | | | 1 2 | C | + | | | 1 2 | D | = | | 0 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | | 11 20 | B | + | | | 59 100 | C | | - | 41 100 | D | = | | 0 | | (2) |
| | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | + | | | 209 100 | D | = | | 0 | | (3) |
| | | 109 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | - | 9 100 | D | = | | 0 | | (4) |
|
Multiply both sides of equation (1) by 9 Divide the two sides of equation (1) by 100, the equation can be obtained: | | | 9 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | + | | | 9 100 | D | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | | 11 20 | B | + | | | 59 100 | C | | - | 41 100 | D | = | | 0 | | (2) |
| | | | 109 100 | A | + | | | 9 100 | B | + | | | 9 100 | C | | - | 9 100 | D | = | | 0 | | (4) |
|
Multiply both sides of equation (1) by 109 Divide the two sides of equation (1) by 100, the equation can be obtained: | | | 109 100 | A | + | | | 109 100 | B | + | | | 109 100 | C | + | | | 109 100 | D | = | | 0 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | | 11 20 | B | + | | | 59 100 | C | | - | 41 100 | D | = | | 0 | | (2) |
| | |
Multiply both sides of equation (2) by 20 Divide the two sides of equation (2) by 11, the equation can be obtained: | | B | + | | | 59 55 | C | | - | 41 55 | D | = | | 0 | (8) | , then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
| | | | | | 11 20 | B | + | | | 59 100 | C | | - | 41 100 | D | = | | 0 | | (2) |
| | |
交After the exchange of equation (3) and equation (4), the equation system becomes:
| | | | | | 11 20 | B | + | | | 59 100 | C | | - | 41 100 | D | = | | 0 | | (2) |
| | |
Multiply both sides of equation (4) by 1059 Divide both sides of equation (4) by 1100, get the equation:, then add the two sides of equation (9) to both sides of equation (3), get the equation:
| | | | | | 11 20 | B | + | | | 59 100 | C | | - | 41 100 | D | = | | 0 | | (2) |
| | |
Multiply both sides of equation (4) by 41 Divide both sides of equation (4) by 200, get the equation:, then add the two sides of equation (10) to both sides of equation (2), get the equation:
Divide both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (11) from both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 649 Divide both sides of equation (3) by 80, get the equation:, then subtract both sides of equation (12) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 55 Divide both sides of equation (3) by 4, get the equation:, then subtract both sides of equation (13) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 20 Divide both sides of equation (2) by 11, get the equation:, then subtract both sides of equation (14) from 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》 |