detailed information: The input equation set is:
| | | | | A | | -1 | B | | -3 | C | + | | D | | -3 | E | = | | 2 | | (2) |
| | 2 | A | | -3 | B | + | | 4 | C | | -5 | D | + | | 2 | E | = | | 7 | | (3) |
| | 9 | A | | -9 | B | + | | 6 | C | | -16 | D | + | | E | = | | 25 | | (4) |
| | Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | | | 2 | A | | -3 | B | + | | 4 | C | | -5 | D | + | | 2 | E | = | | 7 | | (3) |
| | 9 | A | | -9 | B | + | | 6 | C | | -16 | D | + | | E | = | | 25 | | (4) |
| |
Multiply both sides of equation (1) by 2, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | | | 9 | A | | -9 | B | + | | 6 | C | | -16 | D | + | | E | = | | 25 | | (4) |
| |
Multiply both sides of equation (1) by 9, the equation can be obtained: | | 9 | A | + | | 18 | B | | -27 | D | + | | 18 | E | = | | 9 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | | -27 | B | + | | 6 | C | + | | 11 | D | | -17 | E | = | | 16 | | (4) |
| |
Multiply both sides of equation (2) by 7 Divide the two sides of equation (2) by 3, the equation can be obtained: | -7 | B | | -7 | C | + | | | 28 3 | D | | - | 35 3 | E | = | | | 7 3 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | | | 11 | C | | - | 25 3 | D | + | | | 29 3 | E | = | | | 8 3 | | (3) |
| -27 | B | + | | 6 | C | + | | 11 | D | | -17 | E | = | | 16 | | (4) |
| |
Multiply both sides of equation (2) by 9, the equation can be obtained: | -27 | B | | -27 | C | + | | 36 | D | | -45 | E | = | | 9 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | | | 11 | C | | - | 25 3 | D | + | | | 29 3 | E | = | | | 8 3 | | (3) |
| | |
Multiply both sides of equation (3) by 3, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | | | 11 | C | | - | 25 3 | D | + | | | 29 3 | E | = | | | 8 3 | | (3) |
| | |
Multiply both sides of equation (4) by 29 Divide both sides of equation (4) by 3, get the equation:, then add the two sides of equation (11) to both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 5, get the equation:, then subtract both sides of equation (12) from both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 2, get the equation:, then add the two sides of equation (13) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 3 Divide both sides of equation (3) by 11, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
Multiply both sides of equation (2) by 2 Divide both sides of equation (2) by 3, 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:
Convert the solution of the equation set to decimals:
Where: D are arbitrary constants. 解方程组的详细方法请参阅:《多元一次方程组的解法》 |