detailed information: The input equation set is:
| | | | 2 | A | | -2 | B | + | | 3 | C | + | | 4 | D | = | | 33 | | (1) |
| | | | 5 | A | + | | 4 | B | + | | 6 | C | | -2 | D | = | | 45 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 2, the equation can be obtained: | | 3 | A | | -3 | B | + | | | 9 2 | C | + | | 6 | D | = | | | 99 2 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | 2 | A | | -2 | B | + | | 3 | C | + | | 4 | D | = | | 33 | | (1) |
| -2 | B | | - | 23 2 | C | | -3 | D | = | | - | 77 2 | | (2) |
| | | 5 | A | + | | 4 | B | + | | 6 | C | | -2 | D | = | | 45 | | (4) |
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Multiply both sides of equation (1) by 2, the equation can be obtained: | | 4 | A | | -4 | B | + | | 6 | C | + | | 8 | D | = | | 66 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | 2 | A | | -2 | B | + | | 3 | C | + | | 4 | D | = | | 33 | | (1) |
| -2 | B | | - | 23 2 | C | | -3 | D | = | | - | 77 2 | | (2) |
| | | 5 | A | + | | 4 | B | + | | 6 | C | | -2 | D | = | | 45 | | (4) |
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Multiply both sides of equation (1) by 5 Divide the two sides of equation (1) by 2, the equation can be obtained: | | 5 | A | | -5 | B | + | | | 15 2 | C | + | | 10 | D | = | | | 165 2 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | 2 | A | | -2 | B | + | | 3 | C | + | | 4 | D | = | | 33 | | (1) |
| -2 | B | | - | 23 2 | C | | -3 | D | = | | - | 77 2 | | (2) |
| | | 9 | B | | - | 3 2 | C | | -12 | D | = | | - | 75 2 | | (4) |
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Multiply both sides of equation (2) by 7 Divide the two sides of equation (2) by 2, the equation can be obtained: | -7 | B | | - | 161 4 | C | | - | 21 2 | D | = | | - | 539 4 | (8) | , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | | 2 | A | | -2 | B | + | | 3 | C | + | | 4 | D | = | | 33 | | (1) |
| -2 | B | | - | 23 2 | C | | -3 | D | = | | - | 77 2 | | (2) |
| - | 201 4 | C | | - | 47 2 | D | = | | - | 791 4 | | (3) |
| | 9 | B | | - | 3 2 | C | | -12 | D | = | | - | 75 2 | | (4) |
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Multiply both sides of equation (2) by 9 Divide the two sides of equation (2) by 2, the equation can be obtained: | -9 | B | | - | 207 4 | C | | - | 27 2 | D | = | | - | 693 4 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
| | | | 2 | A | | -2 | B | + | | 3 | C | + | | 4 | D | = | | 33 | | (1) |
| -2 | B | | - | 23 2 | C | | -3 | D | = | | - | 77 2 | | (2) |
| - | 201 4 | C | | - | 47 2 | D | = | | - | 791 4 | | (3) |
| - | 213 4 | C | | - | 51 2 | D | = | | - | 843 4 | | (4) |
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Multiply both sides of equation (3) by 71 Divide the two sides of equation (3) by 67, the equation can be obtained: | - | 213 4 | C | | - | 3337 134 | D | = | | - | 56161 268 | (10) | , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | 2 | A | | -2 | B | + | | 3 | C | + | | 4 | D | = | | 33 | | (1) |
| -2 | B | | - | 23 2 | C | | -3 | D | = | | - | 77 2 | | (2) |
| - | 201 4 | C | | - | 47 2 | D | = | | - | 791 4 | | (3) |
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Multiply both sides of equation (4) by 3149 Divide both sides of equation (4) by 80, get the equation:, then subtract both sides of equation (11) from both sides of equation (3), get the equation:
| | | | 2 | A | | -2 | B | + | | 3 | C | + | | 4 | D | = | | 33 | | (1) |
| -2 | B | | - | 23 2 | C | | -3 | D | = | | - | 77 2 | | (2) |
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Multiply both sides of equation (4) by 201 Divide both sides of equation (4) by 40, get the equation:, then subtract both sides of equation (12) from both sides of equation (2), get the equation:
| | | | 2 | A | | -2 | B | + | | 3 | C | + | | 4 | D | = | | 33 | | (1) |
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Multiply both sides of equation (4) by 67 Divide both sides of equation (4) by 10, 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 46 Divide both sides of equation (3) by 201, get the equation:, then subtract both sides of equation (14) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 4 Divide both sides of equation (3) by 67, get the equation:, then add the two sides of equation (15) to both sides of equation (1), get the equation:
Subtract both sides of equation (2) from 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》 |