detailed information: The input equation set is:
| | | | | 27 | A | + | | 9 | B | + | | 3 | C | + | | D | = | | 2 | | (2) |
| | 64 | A | + | | 16 | B | + | | 4 | C | + | | D | = | | 4 | | (3) |
| | 125 | A | + | | 25 | B | + | | 5 | C | + | | D | = | | 5 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 27 Divide the two sides of equation (1) by 8, the equation can be obtained: | | 27 | A | + | | | 27 2 | B | + | | | 27 4 | C | + | | | 27 8 | D | = | | | 27 8 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | - | 9 2 | B | | - | 15 4 | C | | - | 19 8 | D | = | | - | 11 8 | | (2) |
| | 64 | A | + | | 16 | B | + | | 4 | C | + | | D | = | | 4 | | (3) |
| | 125 | A | + | | 25 | B | + | | 5 | C | + | | D | = | | 5 | | (4) |
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Multiply both sides of equation (1) by 8, the equation can be obtained: | | 64 | A | + | | 32 | B | + | | 16 | C | + | | 8 | D | = | | 8 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | - | 9 2 | B | | - | 15 4 | C | | - | 19 8 | D | = | | - | 11 8 | | (2) |
| | | 125 | A | + | | 25 | B | + | | 5 | C | + | | D | = | | 5 | | (4) |
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Multiply both sides of equation (1) by 125 Divide the two sides of equation (1) by 8, the equation can be obtained: | | 125 | A | + | | | 125 2 | B | + | | | 125 4 | C | + | | | 125 8 | D | = | | | 125 8 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | - | 9 2 | B | | - | 15 4 | C | | - | 19 8 | D | = | | - | 11 8 | | (2) |
| | - | 75 2 | B | | - | 105 4 | C | | - | 117 8 | D | = | | - | 85 8 | | (4) |
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Multiply both sides of equation (2) by 32 Divide the two sides of equation (2) by 9, the equation can be obtained: | -16 | B | | - | 40 3 | C | | - | 76 9 | D | = | | - | 44 9 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | - | 9 2 | B | | - | 15 4 | C | | - | 19 8 | D | = | | - | 11 8 | | (2) |
| | - | 75 2 | B | | - | 105 4 | C | | - | 117 8 | D | = | | - | 85 8 | | (4) |
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Multiply both sides of equation (2) by 25 Divide the two sides of equation (2) by 3, the equation can be obtained: | - | 75 2 | B | | - | 125 4 | C | | - | 475 24 | D | = | | - | 275 24 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | - | 9 2 | B | | - | 15 4 | C | | - | 19 8 | D | = | | - | 11 8 | | (2) |
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Multiply both sides of equation (3) by 15 Divide the two sides of equation (3) by 4, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
| | | | - | 9 2 | B | | - | 15 4 | C | | - | 19 8 | D | = | | - | 11 8 | | (2) |
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Multiply both sides of equation (4) by 52 Divide both sides of equation (4) by 9, get the equation:, then add the two sides of equation (11) to both sides of equation (3), get the equation:
| | | | - | 9 2 | B | | - | 15 4 | C | | - | 19 8 | D | = | | - | 11 8 | | (2) |
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Multiply both sides of equation (4) by 19 Divide both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (12) from both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 4, 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 45 Divide both sides of equation (3) by 16, 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 3 Divide both sides of equation (3) by 2, 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 8 Divide both sides of equation (2) by 9, 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》 |