detailed information: The input equation set is:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| | A | + | | | 7 100 | B | + | | | 7 100 | C | + | | E | = | | 0 | | (2) |
| | | | Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | 0 | | (2) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | 0 | | (2) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | 0 | | (3) |
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Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | 0 | | (2) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | 0 | | (3) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | 0 | | (4) |
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Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | 0 | | (2) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | 0 | | (3) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | 0 | | (4) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | 0 | | (5) |
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Multiply both sides of equation (2) by 79 Divide the two sides of equation (2) by 72, the equation can be obtained: | - | 79 100 | B | | - | 79 144 | C | | - | 8453 7200 | D | | - | 553 7200 | E | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | 0 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (3) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | 0 | | (4) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | 0 | | (5) |
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Multiply both sides of equation (2) by 79 Divide the two sides of equation (2) by 72, the equation can be obtained: | - | 79 100 | B | | - | 79 144 | C | | - | 8453 7200 | D | | - | 553 7200 | E | = | | 0 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | 0 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (3) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (4) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | 0 | | (5) |
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Multiply both sides of equation (2) by 79 Divide the two sides of equation (2) by 72, the equation can be obtained: | - | 79 100 | B | | - | 79 144 | C | | - | 8453 7200 | D | | - | 553 7200 | E | = | | 0 | (8) | , then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | 0 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (3) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (4) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (5) |
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Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | 0 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (3) |
| | - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (5) |
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Subtract both sides of equation (3) from both sides of equation (5) ,the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | 0 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (3) |
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Multiply both sides of equation (3) by 1800 Divide both sides of equation (3) by 77, get the equation: | - | 1 2 | C | + | | | 107 44 | D | | - | 7151 308 | E | = | | 0 | (9) | , then subtract both sides of equation (9) from both sides of equation (2), get the equation:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 963 275 | D | + | | | 44559 1925 | E | = | | 0 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (3) |
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Multiply both sides of equation (3) by 2052 Divide both sides of equation (3) by 77, get the equation: | - | 57 100 | C | + | | | 6099 2200 | D | | - | 407607 15400 | E | = | | 0 | (10) | , then add the two sides of equation (10) to both sides of equation (1), get the equation:
| | | | A | + | | | 79 100 | B | + | | | 8453 2200 | D | | - | 391129 15400 | E | = | | 0 | | (1) |
| - | 18 25 | B | | - | 963 275 | D | + | | | 44559 1925 | E | = | | 0 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | 0 | | (3) |
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Multiply both sides of equation (2) by 79 Divide both sides of equation (2) by 72, get the equation: | - | 79 100 | B | | - | 8453 2200 | D | + | | | 391129 15400 | E | = | | 0 | (11) | , then add the two sides of equation (11) to both sides of equation (1), get the equation:
| | | | - | 18 25 | B | | - | 963 275 | D | + | | | 44559 1925 | E | = | | 0 | | (2) |
| | C | | - | 107 22 | D | + | | | 7151 154 | E | = | | 0 | | (3) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
| | | | | B | + | | | 107 22 | D | | - | 4951 154 | E | = | | 0 | | (2) |
| | C | | - | 107 22 | D | + | | | 7151 154 | E | = | | 0 | | (3) |
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Therefore, the solution of the equation set is:
Where: D, E 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》 |