detailed information: The input equation set is:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| | A | + | | | 2 5 | B | + | | | 97 5 | C | + | | | 47 5 | D | + | | | 32 5 | E | = | | | 7 5 | | (2) |
| | A | + | | | 2 5 | B | + | | | 102 5 | C | + | | | 52 5 | D | + | | | 32 5 | E | = | | | 7 5 | | (3) |
| | A | + | | | 2 5 | B | + | | | 112 5 | C | + | | 11 | D | + | | 7 | E | = | | | 7 5 | | (4) |
| | A | + | | | 2 5 | B | + | | | 122 5 | C | + | | | 52 5 | D | + | | | 37 5 | E | = | | | 7 5 | | (5) |
| Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| | A | + | | | 2 5 | B | + | | | 102 5 | C | + | | | 52 5 | D | + | | | 32 5 | E | = | | | 7 5 | | (3) |
| | A | + | | | 2 5 | B | + | | | 112 5 | C | + | | 11 | D | + | | 7 | E | = | | | 7 5 | | (4) |
| | A | + | | | 2 5 | B | + | | | 122 5 | C | + | | | 52 5 | D | + | | | 37 5 | E | = | | | 7 5 | | (5) |
|
Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| - | 1 2 | B | + | | | 14 5 | C | + | | | 13 10 | D | + | | | 19 10 | E | = | | 0 | | (3) |
| | A | + | | | 2 5 | B | + | | | 112 5 | C | + | | 11 | D | + | | 7 | E | = | | | 7 5 | | (4) |
| | A | + | | | 2 5 | B | + | | | 122 5 | C | + | | | 52 5 | D | + | | | 37 5 | E | = | | | 7 5 | | (5) |
|
Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| - | 1 2 | B | + | | | 14 5 | C | + | | | 13 10 | D | + | | | 19 10 | E | = | | 0 | | (3) |
| - | 1 2 | B | + | | | 24 5 | C | + | | | 19 10 | D | + | | | 5 2 | E | = | | 0 | | (4) |
| | A | + | | | 2 5 | B | + | | | 122 5 | C | + | | | 52 5 | D | + | | | 37 5 | E | = | | | 7 5 | | (5) |
|
Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| - | 1 2 | B | + | | | 14 5 | C | + | | | 13 10 | D | + | | | 19 10 | E | = | | 0 | | (3) |
| - | 1 2 | B | + | | | 24 5 | C | + | | | 19 10 | D | + | | | 5 2 | E | = | | 0 | | (4) |
| - | 1 2 | B | + | | | 34 5 | C | + | | | 13 10 | D | + | | | 29 10 | E | = | | 0 | | (5) |
|
Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| | - | 1 2 | B | + | | | 24 5 | C | + | | | 19 10 | D | + | | | 5 2 | E | = | | 0 | | (4) |
| - | 1 2 | B | + | | | 34 5 | C | + | | | 13 10 | D | + | | | 29 10 | E | = | | 0 | | (5) |
|
Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| | | - | 1 2 | B | + | | | 34 5 | C | + | | | 13 10 | D | + | | | 29 10 | E | = | | 0 | | (5) |
|
Subtract both sides of equation (2) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| | | |
Multiply both sides of equation (3) by 3, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| | | |
Multiply both sides of equation (3) by 5, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| | | |
Multiply both sides of equation (4) by 20 Divide the two sides of equation (4) by 7, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| | | |
Multiply both sides of equation (5) by 21 Divide both sides of equation (5) by 25, get the equation:, then add the two sides of equation (9) to both sides of equation (4), get the equation:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | + | | | 19 10 | E | = | | 0 | | (2) |
| | | |
Multiply both sides of equation (5) by 133 Divide both sides of equation (5) by 50, get the equation:, then add the two sides of equation (10) to both sides of equation (2), get the equation:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | + | | | 9 2 | E | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | = | | 0 | | (2) |
| | | |
Multiply both sides of equation (5) by 63 Divide both sides of equation (5) by 10, get the equation:, then add the two sides of equation (11) to both sides of equation (1), get the equation:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | = | | 0 | | (2) |
| | | |
Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 7, get the equation:, then add the two sides of equation (12) to both sides of equation (3), get the equation:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | = | | | 7 5 | | (1) |
| - | 1 2 | B | + | | | 9 5 | C | + | | | 3 10 | D | = | | 0 | | (2) |
| | | |
Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 14, get the equation:, then add the two sides of equation (13) to both sides of equation (2), get the equation:
| | | | A | + | | | 9 10 | B | + | | | 88 5 | C | + | | | 91 10 | D | = | | | 7 5 | | (1) |
| | | | |
Multiply both sides of equation (4) by 13 Divide both sides of equation (4) by 2, 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 (3) by 9 Divide both sides of equation (3) by 5, get the equation:, then subtract both sides of equation (15) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 88 Divide both sides of equation (3) by 5, get the equation:, then subtract both sides of equation (16) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 9 Divide both sides of equation (2) by 5, get the equation:, then add the two sides of equation (17) 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》 |