detailed information: The input equation set is:
| | | | | | 2 | A | + | | 7 | B | + | | 14 | C | + | | D | = | | 1 | | (3) |
| | 7 | A | + | | 6 | B | + | | 42 | C | + | | D | = | | 7 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 6, the equation can be obtained: | | 6 | A | + | | 12 | B | + | | 12 | C | + | | 6 | D | = | | 6 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | | | 2 | A | + | | 7 | B | + | | 14 | C | + | | D | = | | 1 | | (3) |
| | 7 | A | + | | 6 | B | + | | 42 | C | + | | D | = | | 7 | | (4) |
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Multiply both sides of equation (1) by 2, the equation can be obtained: | | 2 | A | + | | 4 | B | + | | 4 | C | + | | 2 | D | = | | 2 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | | | | 7 | A | + | | 6 | B | + | | 42 | C | + | | D | = | | 7 | | (4) |
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Multiply both sides of equation (1) by 7, the equation can be obtained: | | 7 | A | + | | 14 | B | + | | 14 | C | + | | 7 | D | = | | 7 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (2) by 3 Divide the two sides of equation (2) by 11, the equation can be obtained: | -3 | B | | - | 18 11 | C | | - | 15 11 | D | = | | | 3 11 | (8) | , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | | | | | 92 11 | C | | - | 26 11 | D | = | | - | 8 11 | | (3) |
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Multiply both sides of equation (2) by 8 Divide the two sides of equation (2) by 11, the equation can be obtained: | -8 | B | | - | 48 11 | C | | - | 40 11 | D | = | | | 8 11 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | | | | 92 11 | C | | - | 26 11 | D | = | | - | 8 11 | | (3) |
| | | 356 11 | C | | - | 26 11 | D | = | | - | 8 11 | | (4) |
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Multiply both sides of equation (3) by 89 Divide the two sides of equation (3) by 23, the equation can be obtained: | | | 356 11 | C | | - | 2314 253 | D | = | | - | 712 253 | (10) | , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | | | | 92 11 | C | | - | 26 11 | D | = | | - | 8 11 | | (3) |
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Multiply both sides of equation (4) by 23 Divide both sides of equation (4) by 66, 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 115 Divide both sides of equation (4) by 156, get the equation:, then add the two sides of equation (12) to both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 23 Divide both sides of equation (4) by 156, get the equation:, then subtract both sides of equation (13) from both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 33 Divide both sides of equation (3) by 46, 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 (3) by 11 Divide both sides of equation (3) by 46, get the equation:, then subtract both sides of equation (15) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 2 Divide both sides of equation (2) by 11, 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》 |