detailed information: The input equation set is:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | - | 207 100 | | (1) |
| | A | + | | | 7 100 | B | + | | | 7 100 | C | + | | E | = | | -2 | | (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 | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (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 | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (2) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | - | 93 100 | | (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 | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (2) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | - | 93 100 | | (3) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | - | 93 100 | | (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 | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (2) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | - | 93 100 | | (3) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | - | 93 100 | | (4) |
| | | 21 100 | B | | - | 57 100 | C | | - | 7 100 | D | | - | 7 100 | E | = | | | 7 100 | | (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 | = | | | 553 7200 | (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 | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | - | 7249 7200 | | (3) |
| - | 79 100 | B | | - | 57 100 | C | | - | 107 100 | D | | - | 107 100 | E | = | | - | 93 100 | | (4) |
| | | 21 100 | B | | - | 57 100 | C | | - | 7 100 | D | | - | 7 100 | E | = | | | 7 100 | | (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 | = | | | 553 7200 | (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 | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | - | 7249 7200 | | (3) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | - | 7249 7200 | | (4) |
| | | 21 100 | B | | - | 57 100 | C | | - | 7 100 | D | | - | 7 100 | E | = | | | 7 100 | | (5) |
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Multiply both sides of equation (2) by 7 Divide the two sides of equation (2) by 24, the equation can be obtained: | - | 21 100 | B | | - | 7 48 | C | | - | 749 2400 | D | | - | 49 2400 | E | = | | | 49 2400 | (8) | , then add the two sides of equation (8) to both sides of equation (5), the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | - | 7249 7200 | | (3) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | - | 7249 7200 | | (4) |
| - | 859 1200 | C | | - | 917 2400 | D | | - | 217 2400 | E | = | | | 217 2400 | | (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 | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | - | 7249 7200 | | (3) |
| | - | 859 1200 | C | | - | 917 2400 | D | | - | 217 2400 | E | = | | | 217 2400 | | (5) |
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Multiply both sides of equation (3) by 2577 Divide the two sides of equation (3) by 77, the equation can be obtained: | - | 859 1200 | C | + | | | 91913 26400 | D | | - | 6142709 184800 | E | = | | - | 566081 16800 | (9) | , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | - | 7249 7200 | | (3) |
| | - | 85 22 | D | + | | | 5105 154 | E | = | | | 473 14 | | (5) |
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交After the exchange of equation (4) and equation (5), the equation system becomes:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (2) |
| - | 77 3600 | C | + | | | 749 7200 | D | | - | 7151 7200 | E | = | | - | 7249 7200 | | (3) |
| - | 85 22 | D | + | | | 5105 154 | E | = | | | 473 14 | | (4) |
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Multiply both sides of equation (4) by 8239 Divide both sides of equation (4) by 306000, get the equation: | - | 749 7200 | D | + | | | 109247 122400 | E | = | | | 556721 612000 | (10) | , then add the two sides of equation (10) to both sides of equation (3), get the equation:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 107 100 | D | | - | 7 100 | E | = | | | 7 100 | | (2) |
| - | 77 3600 | C | | - | 77 765 | E | = | | - | 14861 153000 | | (3) |
| - | 85 22 | D | + | | | 5105 154 | E | = | | | 473 14 | | (4) |
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Multiply both sides of equation (4) by 1177 Divide both sides of equation (4) by 4250, get the equation: | - | 107 100 | D | + | | | 109247 11900 | E | = | | | 556721 59500 | (11) | , then subtract both sides of equation (11) from both sides of equation (2), get the equation:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 107 100 | D | + | | | 107 100 | E | = | | - | 207 100 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 5504 595 | E | = | | - | 138139 14875 | | (2) |
| - | 77 3600 | C | | - | 77 765 | E | = | | - | 14861 153000 | | (3) |
| - | 85 22 | D | + | | | 5105 154 | E | = | | | 473 14 | | (4) |
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Multiply both sides of equation (4) by 1177 Divide both sides of equation (4) by 4250, get the equation: | - | 107 100 | D | + | | | 109247 11900 | E | = | | | 556721 59500 | (12) | , then add the two sides of equation (12) to both sides of equation (1), get the equation:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 6099 595 | E | = | | | 108389 14875 | | (1) |
| - | 18 25 | B | | - | 1 2 | C | | - | 5504 595 | E | = | | - | 138139 14875 | | (2) |
| - | 77 3600 | C | | - | 77 765 | E | = | | - | 14861 153000 | | (3) |
| - | 85 22 | D | + | | | 5105 154 | E | = | | | 473 14 | | (4) |
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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 | | - | 40 17 | E | = | | - | 193 85 | (13) | , then subtract both sides of equation (13) from both sides of equation (2), get the equation:
| | | | A | + | | | 79 100 | B | + | | | 57 100 | C | + | | | 6099 595 | E | = | | | 108389 14875 | | (1) |
| - | 18 25 | B | | - | 4104 595 | E | = | | - | 104364 14875 | | (2) |
| - | 77 3600 | C | | - | 77 765 | E | = | | - | 14861 153000 | | (3) |
| | D | | - | 1021 119 | E | = | | - | 5203 595 | | (4) |
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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 | | - | 228 85 | E | = | | - | 11001 4250 | (14) | , then add the two sides of equation (14) to both sides of equation (1), get the equation:
| | | | A | + | | | 79 100 | B | + | | | 4503 595 | E | = | | | 139771 29750 | | (1) |
| - | 18 25 | B | | - | 4104 595 | E | = | | - | 104364 14875 | | (2) |
| - | 77 3600 | C | | - | 77 765 | E | = | | - | 14861 153000 | | (3) |
| | D | | - | 1021 119 | E | = | | - | 5203 595 | | (4) |
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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 | | - | 4503 595 | E | = | | - | 229021 29750 | (15) | , then add the two sides of equation (15) to both sides of equation (1), get the equation:
| | | | - | 18 25 | B | | - | 4104 595 | E | = | | - | 104364 14875 | | (2) |
| | | D | | - | 1021 119 | E | = | | - | 5203 595 | | (4) |
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The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
| | | | | B | + | | | 1140 119 | E | = | | | 5798 595 | | (2) |
| | | D | | - | 1021 119 | E | = | | - | 5203 595 | | (4) |
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Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
Where: 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》 |