detailed information: The input equation set is:
| | | | | - | 3 2 | B | + | | | 6 5 | C | + | | E | + | | F | = | | 0 | | (3) |
| | | | Question solving process:
Multiply both sides of equation (1) by 6 Divide the two sides of equation (1) by 5, the equation can be obtained: , then add the two sides of equation (7) to both sides of equation (2), the equations are reduced to:
| | | | | - | 3 2 | B | + | | | 6 5 | C | + | | E | + | | F | = | | 0 | | (3) |
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Multiply both sides of equation (2) by 5 Divide the two sides of equation (2) by 4, the equation can be obtained: , then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
| | | | | | | 49 20 | C | + | | | 5 4 | D | + | | E | + | | F | = | | 45 | | (3) |
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Multiply both sides of equation (3) by 20 Divide both sides of equation (3) by 49, get the equation: | | C | + | | | 25 49 | D | + | | | 20 49 | E | + | | | 20 49 | F | = | | | 900 49 | (9) | , then subtract both sides of equation (9) from both sides of equation (2), get the equation:
| | | | | | 6 5 | B | + | | | 24 49 | D | | - | 20 49 | E | | - | 20 49 | F | = | | | 864 49 | | (2) |
| | | 49 20 | C | + | | | 5 4 | D | + | | E | + | | F | = | | 45 | | (3) |
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Multiply both sides of equation (2) by 5 Divide both sides of equation (2) by 6, get the equation: | | B | + | | | 20 49 | D | | - | 50 147 | E | | - | 50 147 | F | = | | | 720 49 | (10) | , then subtract both sides of equation (10) from both sides of equation (1), get the equation:
| | | | A | | - | 20 49 | D | + | | | 50 147 | E | + | | | 50 147 | F | = | | | 750 49 | | (1) |
| | | 6 5 | B | + | | | 24 49 | D | | - | 20 49 | E | | - | 20 49 | F | = | | | 864 49 | | (2) |
| | C | + | | | 25 49 | D | + | | | 20 49 | E | + | | | 20 49 | F | = | | | 900 49 | | (3) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
| | | | A | | - | 20 49 | D | + | | | 50 147 | E | + | | | 50 147 | F | = | | | 750 49 | | (1) |
| | B | + | | | 20 49 | D | | - | 50 147 | E | | - | 50 147 | F | = | | | 720 49 | | (2) |
| | C | + | | | 25 49 | D | + | | | 20 49 | E | + | | | 20 49 | F | = | | | 900 49 | | (3) |
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Therefore, the solution of the equation set is:
| | | A = | | | 750 49 | + | | | 20 49 | D | - | | | 50 147 | E | - | | | 50 147 | F |
| B = | | | 720 49 | - | | | 20 49 | D | + | | | 50 147 | E | + | | | 50 147 | F |
| C = | | | 900 49 | - | | | 25 49 | D | - | | | 20 49 | E | - | | | 20 49 | F |
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Convert the solution of the equation set to decimals:
| | | A = | | 15.306122 | + | | | 20 49 | D | - | | | 50 147 | E | - | | | 50 147 | F |
| B = | | 14.693878 | - | | | 20 49 | D | + | | | 50 147 | E | + | | | 50 147 | F |
| C = | | 18.367347 | - | | | 25 49 | D | - | | | 20 49 | E | - | | | 20 49 | F |
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Where: D, E, F are arbitrary constants. 解方程组的详细方法请参阅:《多元一次方程组的解法》 |