detailed information: The input equation set is:
| | | | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | = | | 400 | | (1) |
| | 2 | A | + | | 3 | B | + | | 4 | C | + | | D | = | | 600 | | (2) |
| | 3 | A | + | | 4 | B | + | | C | + | | 2 | D | = | | 800 | | (3) |
| | 4 | A | + | | B | + | | 2 | C | + | | 3 | D | = | | 1000 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 2, the equation can be obtained: | | 2 | A | + | | 4 | B | + | | 6 | C | + | | 8 | D | = | | 800 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | = | | 400 | | (1) |
| | | 3 | A | + | | 4 | B | + | | C | + | | 2 | D | = | | 800 | | (3) |
| | 4 | A | + | | B | + | | 2 | C | + | | 3 | D | = | | 1000 | | (4) |
|
Multiply both sides of equation (1) by 3, the equation can be obtained: | | 3 | A | + | | 6 | B | + | | 9 | C | + | | 12 | D | = | | 1200 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | = | | 400 | | (1) |
| | | | 4 | A | + | | B | + | | 2 | C | + | | 3 | D | = | | 1000 | | (4) |
|
Multiply both sides of equation (1) by 4, the equation can be obtained: | | 4 | A | + | | 8 | B | + | | 12 | C | + | | 16 | D | = | | 1600 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | = | | 400 | | (1) |
| | | |
Multiply both sides of equation (2) by 2, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | = | | 400 | | (1) |
| | | |
Multiply both sides of equation (2) by 7, the equation can be obtained: | -7 | B | | -14 | C | | -49 | D | = | | -1400 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | = | | 400 | | (1) |
| | | |
Add both sides of equation (3) to both sides of equation (4) ,the equations are reduced to:
| | | | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | = | | 400 | | (1) |
| | | |
Divide both sides of equation (4) by 10, get the equation:, then subtract both sides of equation (10) from both sides of equation (3), get the equation:
| | | | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | = | | 400 | | (1) |
| | | |
Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 40, get the equation:, then add the two sides of equation (11) to both sides of equation (2), get the equation:
| | | | A | + | | 2 | B | + | | 3 | C | + | | 4 | D | = | | 400 | | (1) |
| | | |
Divide both sides of equation (4) by 10, get the equation:, then subtract both sides of equation (12) from both sides of equation (1), get the equation:
Divide both sides of equation (3) by 2, get the equation:, then subtract both sides of equation (13) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 3 Divide both sides of equation (3) by 4, get the equation:, then add the two sides of equation (14) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 2, get the equation:, then add the two sides of equation (15) to 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》 |