detailed information: The input equation set is:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
| | | A | + | | B | + | | 2 | C | | -1 | D | | -1 | E | = | | -2 | | (3) |
| | | Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
| | | A | + | | B | + | | 2 | C | | -1 | D | | -1 | E | = | | -2 | | (3) |
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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 | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
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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 | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
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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 | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
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Subtract both sides of equation (2) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
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交After the exchange of equation (3) and equation (4), the equation system becomes:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
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Divide the two sides of equation (4) by 2, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
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Add both sides of equation (5) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
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Multiply both sides of equation (5) by 3 Divide both sides of equation (5) by 4, get the equation:, then add the two sides of equation (7) to both sides of equation (3), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
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Add both sides of equation (5) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | 2 | C | + | | 3 | D | + | | 3 | E | = | | 6 | | (1) |
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Multiply both sides of equation (5) by 3 Divide both sides of equation (5) by 4, get the equation:, then subtract both sides of equation (8) from both sides of equation (1), get the equation:
Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 4, get the equation:, then subtract both sides of equation (9) from both sides of equation (3), get the equation:
Divide both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (10) from both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 3 Divide both sides of equation (4) by 4, get the equation:, then add the two sides of equation (11) 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 (12) 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 (13) 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 (14) 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |