detailed information: The input equation set is:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | | | Question solving process:
Divide the two sides of equation (1) by 140, the equation can be obtained: | | | 1 10 | A | | - | 3 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 6 7 | (6) | , then add the two sides of equation (6) to both sides of equation (2), the equations are reduced to:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| | | |
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 14, the equation can be obtained: | | 3 | A | | - | 9 14 | B | + | | | 45 7 | D | | - | 45 7 | E | = | | | 180 7 | (7) | , then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| - | 9 14 | B | + | | 5 | C | + | | | 45 7 | D | | - | 45 7 | E | = | | | 12 7 | | (3) |
| | |
Divide the two sides of equation (1) by 14, the equation can be obtained: | | A | | - | 3 14 | B | + | | | 15 7 | D | | - | 15 7 | E | = | | | 60 7 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| - | 9 14 | B | + | | 5 | C | + | | | 45 7 | D | | - | 45 7 | E | = | | | 12 7 | | (3) |
| | | 3 14 | B | | - | 15 7 | D | + | | | 15 7 | E | = | | | 10 7 | | (4) |
| |
Divide the two sides of equation (1) by 14, the equation can be obtained: | | A | | - | 3 14 | B | + | | | 15 7 | D | | - | 15 7 | E | = | | | 60 7 | (9) | , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| - | 9 14 | B | + | | 5 | C | + | | | 45 7 | D | | - | 45 7 | E | = | | | 12 7 | | (3) |
| | | 3 14 | B | | - | 15 7 | D | + | | | 15 7 | E | = | | | 10 7 | | (4) |
| | | 3 14 | B | | -1 | C | | - | 71 7 | D | + | | | 15 7 | E | = | | - | 60 7 | | (5) |
|
Multiply both sides of equation (2) by 30 Divide the two sides of equation (2) by 13, the equation can be obtained: | | | 9 14 | B | + | | | 45 91 | D | | - | 45 91 | E | = | | | 30 7 | (10) | , then add the two sides of equation (10) to both sides of equation (3), the equations are reduced to:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| | 5 | C | + | | | 90 13 | D | | - | 90 13 | E | = | | 6 | | (3) |
| | | 3 14 | B | | - | 15 7 | D | + | | | 15 7 | E | = | | | 10 7 | | (4) |
| | | 3 14 | B | | -1 | C | | - | 71 7 | D | + | | | 15 7 | E | = | | - | 60 7 | | (5) |
|
Multiply both sides of equation (2) by 10 Divide the two sides of equation (2) by 13, the equation can be obtained: | | | 3 14 | B | + | | | 15 91 | D | | - | 15 91 | E | = | | | 10 7 | (11) | , then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| | 5 | C | + | | | 90 13 | D | | - | 90 13 | E | = | | 6 | | (3) |
| | | | 3 14 | B | | -1 | C | | - | 71 7 | D | + | | | 15 7 | E | = | | - | 60 7 | | (5) |
|
Multiply both sides of equation (2) by 10 Divide the two sides of equation (2) by 13, the equation can be obtained: | | | 3 14 | B | + | | | 15 91 | D | | - | 15 91 | E | = | | | 10 7 | (12) | , then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| | 5 | C | + | | | 90 13 | D | | - | 90 13 | E | = | | 6 | | (3) |
| | -1 | C | | - | 134 13 | D | + | | | 30 13 | E | = | | -10 | | (5) |
|
Divide the two sides of equation (3) by 5, the equation can be obtained: | | C | + | | | 18 13 | D | | - | 18 13 | E | = | | | 6 5 | (13) | , then add the two sides of equation (13) to both sides of equation (5), the equations are reduced to:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| | 5 | C | + | | | 90 13 | D | | - | 90 13 | E | = | | 6 | | (3) |
| | - | 116 13 | D | + | | | 12 13 | E | = | | - | 44 5 | | (5) |
|
Multiply both sides of equation (4) by 58 Divide the two sides of equation (4) by 15, the equation can be obtained: | - | 116 13 | D | + | | | 116 13 | E | = | | 0 | (14) | , then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| | 5 | C | + | | | 90 13 | D | | - | 90 13 | E | = | | 6 | | (3) |
| | |
Multiply both sides of equation (5) by 15 Divide both sides of equation (5) by 52, get the equation:, then add the two sides of equation (15) to both sides of equation (4), get the equation:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| | 5 | C | + | | | 90 13 | D | | - | 90 13 | E | = | | 6 | | (3) |
| | |
Multiply both sides of equation (5) by 45 Divide both sides of equation (5) by 52, get the equation:, then subtract both sides of equation (16) from both sides of equation (3), get the equation:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | | - | 3 14 | E | = | | | 13 7 | | (2) |
| | | |
Multiply both sides of equation (5) by 3 Divide both sides of equation (5) by 112, get the equation:, then subtract both sides of equation (17) from both sides of equation (2), get the equation:
| | | | 14 | A | | -3 | B | + | | 30 | D | | -30 | E | = | | 120 | | (1) |
| | | 39 140 | B | + | | | 3 14 | D | = | | | 293 140 | | (2) |
| | | |
Multiply both sides of equation (5) by 15 Divide both sides of equation (5) by 4, get the equation:, then subtract both sides of equation (18) from both sides of equation (1), get the equation:
| | | | | | 39 140 | B | + | | | 3 14 | D | = | | | 293 140 | | (2) |
| | | |
Multiply both sides of equation (4) by 3, get the equation:, then add the two sides of equation (19) to both sides of equation (3), get the equation:
| | | | | | 39 140 | B | + | | | 3 14 | D | = | | | 293 140 | | (2) |
| | | |
Multiply both sides of equation (4) by 13 Divide both sides of equation (4) by 140, get the equation:, then add the two sides of equation (20) to both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 13, get the equation:, then add the two sides of equation (21) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 140 Divide both sides of equation (2) by 13, get the equation:, then add the two sides of equation (22) 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》 |