detailed information: The input equation set is:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | + | | D | = | | -2 | | (1) |
| - | 1 2 | A | + | | | 3 2 | B | | - | 1 2 | C | = | | -3 | | (2) |
| | | Question solving process:
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 7, the equation can be obtained: | | | 1 2 | A | | - | 5 14 | B | | - | 1 7 | C | + | | | 5 7 | D | = | | - | 10 7 | (5) | , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | + | | D | = | | -2 | | (1) |
| | | 8 7 | B | | - | 9 14 | C | + | | | 5 7 | D | = | | - | 31 7 | | (2) |
| | |
Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 7, the equation can be obtained: | | | 1 2 | A | | - | 5 14 | B | | - | 1 7 | C | + | | | 5 7 | D | = | | - | 10 7 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | + | | D | = | | -2 | | (1) |
| | | 8 7 | B | | - | 9 14 | C | + | | | 5 7 | D | = | | - | 31 7 | | (2) |
| - | 6 7 | B | + | | | 13 7 | C | + | | | 5 7 | D | = | | | 25 7 | | (3) |
| |
Multiply both sides of equation (1) by 10 Divide the two sides of equation (1) by 7, the equation can be obtained: | | A | | - | 5 7 | B | | - | 2 7 | C | + | | | 10 7 | D | = | | - | 20 7 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | + | | D | = | | -2 | | (1) |
| | | 8 7 | B | | - | 9 14 | C | + | | | 5 7 | D | = | | - | 31 7 | | (2) |
| - | 6 7 | B | + | | | 13 7 | C | + | | | 5 7 | D | = | | | 25 7 | | (3) |
| | | 5 7 | B | + | | | 2 7 | C | | - | 10 7 | D | = | | - | 15 7 | | (4) |
|
Multiply both sides of equation (2) by 3 Divide the two sides of equation (2) by 4, the equation can be obtained: | | | 6 7 | B | | - | 27 56 | C | + | | | 15 28 | D | = | | - | 93 28 | (8) | , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | + | | D | = | | -2 | | (1) |
| | | 8 7 | B | | - | 9 14 | C | + | | | 5 7 | D | = | | - | 31 7 | | (2) |
| | | | 5 7 | B | + | | | 2 7 | C | | - | 10 7 | D | = | | - | 15 7 | | (4) |
|
Multiply both sides of equation (2) by 5 Divide the two sides of equation (2) by 8, the equation can be obtained: | | | 5 7 | B | | - | 45 112 | C | + | | | 25 56 | D | = | | - | 155 56 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | + | | D | = | | -2 | | (1) |
| | | 8 7 | B | | - | 9 14 | C | + | | | 5 7 | D | = | | - | 31 7 | | (2) |
| | |
Divide the two sides of equation (3) by 2, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | + | | D | = | | -2 | | (1) |
| | | 8 7 | B | | - | 9 14 | C | + | | | 5 7 | D | = | | - | 31 7 | | (2) |
| | |
Divide both sides of equation (4) by 2, get the equation:, then add the two sides of equation (11) to both sides of equation (3), get the equation:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | + | | D | = | | -2 | | (1) |
| | | 8 7 | B | | - | 9 14 | C | + | | | 5 7 | D | = | | - | 31 7 | | (2) |
| | |
Multiply both sides of equation (4) by 2 Divide both sides of equation (4) by 7, get the equation:, then add the two sides of equation (12) to both sides of equation (2), get the equation:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | + | | D | = | | -2 | | (1) |
| | | |
Multiply both sides of equation (4) by 2 Divide both sides of equation (4) by 5, get the equation:, then add the two sides of equation (13) to both sides of equation (1), get the equation:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | = | | - | 9 5 | | (1) |
| | | |
Multiply both sides of equation (3) by 36 Divide both sides of equation (3) by 77, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
| | | | | 7 10 | A | | - | 1 2 | B | | - | 1 5 | C | = | | - | 9 5 | | (1) |
| | | |
Multiply both sides of equation (3) by 8 Divide both sides of equation (3) by 55, get the equation:, then add the two sides of equation (15) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 7 Divide both sides of equation (2) by 16, get the equation:, then add the two sides of equation (16) 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |