detailed information: The input equation set is:
| | | | 2 | A | + | | 2 | B | + | | D | + | | 5 | E | = | | -4 | | (1) |
| | | | | Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | D | + | | 5 | E | = | | -4 | | (1) |
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Divide the two sides of equation (1) by 2, the equation can be obtained: | | A | + | | B | + | | | 1 2 | D | + | | | 5 2 | E | = | | -2 | (6) | , then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | D | + | | 5 | E | = | | -4 | | (1) |
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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 | + | | | 5 2 | D | + | | | 25 2 | E | = | | -10 | (7) | , then subtract both sides of equation (7) from both sides of equation (5), the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | D | + | | 5 | E | = | | -4 | | (1) |
| | | | -5 | B | + | | 4 | C | | - | 5 2 | D | | - | 25 2 | E | = | | 16 | | (5) |
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Divide the two sides of equation (2) by 4, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | D | + | | 5 | E | = | | -4 | | (1) |
| | | | -5 | B | + | | 4 | C | | - | 5 2 | D | | - | 25 2 | E | = | | 16 | | (5) |
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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: | | 5 | B | + | | | 5 4 | D | | - | 25 4 | E | = | | - | 5 4 | (9) | , then add the two sides of equation (9) to both sides of equation (5), the equations are reduced to:
| | | | 2 | A | + | | 2 | B | + | | D | + | | 5 | E | = | | -4 | | (1) |
| | | | | 4 | C | | - | 5 4 | D | | - | 75 4 | E | = | | | 59 4 | | (5) |
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交After the exchange of equation (3) and equation (5), the equation system becomes:
| | | | 2 | A | + | | 2 | B | + | | D | + | | 5 | E | = | | -4 | | (1) |
| | | 4 | C | | - | 5 4 | D | | - | 75 4 | E | = | | | 59 4 | | (3) |
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Multiply both sides of equation (5) by 5 Divide both sides of equation (5) by 16, get the equation:, then add the two sides of equation (10) to both sides of equation (4), get the equation:
| | | | 2 | A | + | | 2 | B | + | | D | + | | 5 | E | = | | -4 | | (1) |
| | | 4 | C | | - | 5 4 | D | | - | 75 4 | E | = | | | 59 4 | | (3) |
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Multiply both sides of equation (5) by 75 Divide both sides of equation (5) by 16, get the equation:, then add the two sides of equation (11) to both sides of equation (3), get the equation:
| | | | 2 | A | + | | 2 | B | + | | D | + | | 5 | E | = | | -4 | | (1) |
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Multiply both sides of equation (5) by 5 Divide both sides of equation (5) by 4, get the equation:, then add the two sides of equation (12) to both sides of equation (2), get the equation:
| | | | 2 | A | + | | 2 | B | + | | D | + | | 5 | E | = | | -4 | | (1) |
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Multiply both sides of equation (5) by 5 Divide both sides of equation (5) by 4, get the equation:, then subtract both sides of equation (13) from both sides of equation (1), get the equation:
Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 3, get the equation:, then subtract both sides of equation (14) from both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 4 Divide both sides of equation (4) by 3, get the equation:, then add the two sides of equation (15) to both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 4 Divide both sides of equation (4) by 3, get the equation:, then add the two sides of equation (16) to both sides of equation (1), get the equation:
Divide both sides of equation (2) by 2, get the equation:, then subtract both sides of equation (17) 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:
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》 |