detailed information: The input equation set is:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
| | A | + | | B | | -1 | C | + | | D | + | | E | | -1 | F | = | | 0 | | (2) |
| | | A | + | | B | + | | 2 | C | | -1 | D | | -1 | E | | -2 | F | = | | 4 | | (4) |
| | A | + | | B | | -1 | C | | -1 | D | | -1 | E | + | | F | = | | -4 | | (5) |
| | Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
| | | | A | + | | B | + | | 2 | C | | -1 | D | | -1 | E | | -2 | F | = | | 4 | | (4) |
| | A | + | | B | | -1 | C | | -1 | D | | -1 | E | + | | F | = | | -4 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
| | | | A | + | | B | + | | 2 | C | | -1 | D | | -1 | E | | -2 | F | = | | 4 | | (4) |
| | A | + | | B | | -1 | C | | -1 | D | | -1 | E | + | | F | = | | -4 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
| | | | | A | + | | B | | -1 | C | | -1 | D | | -1 | E | + | | F | = | | -4 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
| | | | -3 | C | | -2 | D | | -2 | E | | -1 | F | = | | -16 | | (5) |
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Subtract both sides of equation (1) from both sides of equation (6) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
| | | | -3 | C | | -2 | D | | -2 | E | | -1 | F | = | | -16 | | (5) |
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交After the exchange of equation (2) and equation (3), the equation system becomes:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
| | | | -3 | C | | -2 | D | | -2 | E | | -1 | F | = | | -16 | | (5) |
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Subtract both sides of equation (2) from both sides of equation (6) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
| | | | -3 | C | | -2 | D | | -2 | E | | -1 | F | = | | -16 | | (5) |
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Subtract both sides of equation (3) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
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Subtract both sides of equation (4) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
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Subtract both sides of equation (4) from both sides of equation (6) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
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交After the exchange of equation (5) and equation (6), the equation system becomes:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
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Multiply both sides of equation (6) by 2 Divide both sides of equation (6) by 3, get the equation:, then subtract both sides of equation (7) from both sides of equation (5), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
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Multiply both sides of equation (6) by 2 Divide both sides of equation (6) by 3, get the equation:, then add the two sides of equation (8) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
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Divide both sides of equation (6) by 2, get the equation:, then add the two sides of equation (9) to both sides of equation (3), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
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Divide both sides of equation (6) by 3, get the equation:, then add the two sides of equation (10) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | + | | 2 | F | = | | 12 | | (1) |
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Divide both sides of equation (6) by 3, get the equation:, then subtract both sides of equation (11) from both sides of equation (1), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | = | | | 32 3 | | (1) |
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Divide both sides of equation (5) by 2, get the equation:, then add the two sides of equation (12) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | = | | | 32 3 | | (1) |
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Divide both sides of equation (5) by 2, get the equation:, then add the two sides of equation (13) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | D | + | | E | = | | | 32 3 | | (1) |
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Divide both sides of equation (5) by 4, get the equation:, then subtract both sides of equation (14) from both sides of equation (1), get the equation:
Divide both sides of equation (4) by 2, get the equation:, then add the two sides of equation (15) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 3, get the equation:, then subtract both sides of equation (16) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 3, get the equation:, then add the two sides of equation (17) to both sides of equation (1), get the equation:
Divide both sides of equation (2) by 2, get the equation:, then add the two sides of equation (18) 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》 |