detailed information: The input equation set is:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 2 | A | + | | B | | -2 | C | + | | 3 | F | | -2 | G | = | | 0 | | (2) |
| | | A | | -2 | B | + | | C | + | | D | | -1 | E | + | | 2 | F | | -1 | G | = | | 1 | | (3) |
| | -2 | A | | -2 | B | + | | C | + | | D | + | | 2 | E | | -3 | F | | -3 | G | = | | -1 | | (4) |
| | | 2 | A | + | | 3 | B | + | | 2 | C | | -2 | D | + | | E | = | | 1 | | (5) |
| | -2 | B | | -2 | C | + | | 3 | D | | -2 | E | + | | F | + | | 3 | G | = | | -4 | | (6) |
| | -3 | A | | -2 | B | | -2 | C | | -3 | D | + | | 3 | E | + | | F | + | | G | = | | -1 | | (7) |
| Question solving process:
Multiply both sides of equation (1) by 2, the equation can be obtained: | | | 2 | A | | -4 | B | | -6 | E | + | | 4 | F | | -4 | G | = | | -8 | (8) | , then subtract both sides of equation (8) from both sides of equation (2), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | A | | -2 | B | + | | C | + | | D | | -1 | E | + | | 2 | F | | -1 | G | = | | 1 | | (3) |
| | -2 | A | | -2 | B | + | | C | + | | D | + | | 2 | E | | -3 | F | | -3 | G | = | | -1 | | (4) |
| | | 2 | A | + | | 3 | B | + | | 2 | C | | -2 | D | + | | E | = | | 1 | | (5) |
| | -2 | B | | -2 | C | + | | 3 | D | | -2 | E | + | | F | + | | 3 | G | = | | -4 | | (6) |
| | -3 | A | | -2 | B | | -2 | C | | -3 | D | + | | 3 | E | + | | F | + | | G | = | | -1 | | (7) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | -2 | A | | -2 | B | + | | C | + | | D | + | | 2 | E | | -3 | F | | -3 | G | = | | -1 | | (4) |
| | | 2 | A | + | | 3 | B | + | | 2 | C | | -2 | D | + | | E | = | | 1 | | (5) |
| | -2 | B | | -2 | C | + | | 3 | D | | -2 | E | + | | F | + | | 3 | G | = | | -4 | | (6) |
| | -3 | A | | -2 | B | | -2 | C | | -3 | D | + | | 3 | E | + | | F | + | | G | = | | -1 | | (7) |
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Multiply both sides of equation (1) by 2, the equation can be obtained: | | | 2 | A | | -4 | B | | -6 | E | + | | 4 | F | | -4 | G | = | | -8 | (9) | , then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | -6 | B | + | | C | + | | D | | -4 | E | + | | F | | -7 | G | = | | -9 | | (4) |
| | | 2 | A | + | | 3 | B | + | | 2 | C | | -2 | D | + | | E | = | | 1 | | (5) |
| | -2 | B | | -2 | C | + | | 3 | D | | -2 | E | + | | F | + | | 3 | G | = | | -4 | | (6) |
| | -3 | A | | -2 | B | | -2 | C | | -3 | D | + | | 3 | E | + | | F | + | | G | = | | -1 | | (7) |
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Multiply both sides of equation (1) by 2, the equation can be obtained: | | | 2 | A | | -4 | B | | -6 | E | + | | 4 | F | | -4 | G | = | | -8 | (10) | , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | -6 | B | + | | C | + | | D | | -4 | E | + | | F | | -7 | G | = | | -9 | | (4) |
| | | 7 | B | + | | 2 | C | | -2 | D | + | | 7 | E | | -4 | F | + | | 4 | G | = | | 9 | | (5) |
| | -2 | B | | -2 | C | + | | 3 | D | | -2 | E | + | | F | + | | 3 | G | = | | -4 | | (6) |
| | -3 | A | | -2 | B | | -2 | C | | -3 | D | + | | 3 | E | + | | F | + | | G | = | | -1 | | (7) |
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Multiply both sides of equation (1) by 3, the equation can be obtained: | | | 3 | A | | -6 | B | | -9 | E | + | | 6 | F | | -6 | G | = | | -12 | (11) | , then add the two sides of equation (11) to both sides of equation (7), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | -6 | B | + | | C | + | | D | | -4 | E | + | | F | | -7 | G | = | | -9 | | (4) |
| | | 7 | B | + | | 2 | C | | -2 | D | + | | 7 | E | | -4 | F | + | | 4 | G | = | | 9 | | (5) |
| | -2 | B | | -2 | C | + | | 3 | D | | -2 | E | + | | F | + | | 3 | G | = | | -4 | | (6) |
| | -8 | B | | -2 | C | | -3 | D | | -6 | E | + | | 7 | F | | -5 | G | = | | -13 | | (7) |
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Multiply both sides of equation (2) by 6 Divide the two sides of equation (2) by 5, the equation can be obtained: | | | 6 | B | | - | 12 5 | C | + | | | 36 5 | E | | - | 6 5 | F | + | | | 12 5 | G | = | | | 48 5 | (12) | , then add the two sides of equation (12) to both sides of equation (4), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | - | 7 5 | C | + | | D | + | | | 16 5 | E | | - | 1 5 | F | | - | 23 5 | G | = | | | 3 5 | | (4) |
| | | 7 | B | + | | 2 | C | | -2 | D | + | | 7 | E | | -4 | F | + | | 4 | G | = | | 9 | | (5) |
| | -2 | B | | -2 | C | + | | 3 | D | | -2 | E | + | | F | + | | 3 | G | = | | -4 | | (6) |
| | -8 | B | | -2 | C | | -3 | D | | -6 | E | + | | 7 | F | | -5 | G | = | | -13 | | (7) |
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Multiply both sides of equation (2) by 7 Divide the two sides of equation (2) by 5, the equation can be obtained: | | | 7 | B | | - | 14 5 | C | + | | | 42 5 | E | | - | 7 5 | F | + | | | 14 5 | G | = | | | 56 5 | (13) | , then subtract both sides of equation (13) from both sides of equation (5), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | - | 7 5 | C | + | | D | + | | | 16 5 | E | | - | 1 5 | F | | - | 23 5 | G | = | | | 3 5 | | (4) |
| | | | 24 5 | C | | -2 | D | | - | 7 5 | E | | - | 13 5 | F | + | | | 6 5 | G | = | | - | 11 5 | | (5) |
| | -2 | B | | -2 | C | + | | 3 | D | | -2 | E | + | | F | + | | 3 | G | = | | -4 | | (6) |
| | -8 | B | | -2 | C | | -3 | D | | -6 | E | + | | 7 | F | | -5 | G | = | | -13 | | (7) |
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Multiply both sides of equation (2) by 2 Divide the two sides of equation (2) by 5, the equation can be obtained: | | | 2 | B | | - | 4 5 | C | + | | | 12 5 | E | | - | 2 5 | F | + | | | 4 5 | G | = | | | 16 5 | (14) | , then add the two sides of equation (14) to both sides of equation (6), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | - | 7 5 | C | + | | D | + | | | 16 5 | E | | - | 1 5 | F | | - | 23 5 | G | = | | | 3 5 | | (4) |
| | | | 24 5 | C | | -2 | D | | - | 7 5 | E | | - | 13 5 | F | + | | | 6 5 | G | = | | - | 11 5 | | (5) |
| | - | 14 5 | C | + | | 3 | D | + | | | 2 5 | E | + | | | 3 5 | F | + | | | 19 5 | G | = | | - | 4 5 | | (6) |
| | -8 | B | | -2 | C | | -3 | D | | -6 | E | + | | 7 | F | | -5 | G | = | | -13 | | (7) |
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Multiply both sides of equation (2) by 8 Divide the two sides of equation (2) by 5, the equation can be obtained: | | | 8 | B | | - | 16 5 | C | + | | | 48 5 | E | | - | 8 5 | F | + | | | 16 5 | G | = | | | 64 5 | (15) | , then add the two sides of equation (15) to both sides of equation (7), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | - | 7 5 | C | + | | D | + | | | 16 5 | E | | - | 1 5 | F | | - | 23 5 | G | = | | | 3 5 | | (4) |
| | | | 24 5 | C | | -2 | D | | - | 7 5 | E | | - | 13 5 | F | + | | | 6 5 | G | = | | - | 11 5 | | (5) |
| | - | 14 5 | C | + | | 3 | D | + | | | 2 5 | E | + | | | 3 5 | F | + | | | 19 5 | G | = | | - | 4 5 | | (6) |
| | - | 26 5 | C | | -3 | D | + | | | 18 5 | E | + | | | 27 5 | F | | - | 9 5 | G | = | | - | 1 5 | | (7) |
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Multiply both sides of equation (3) by 7 Divide the two sides of equation (3) by 5, the equation can be obtained: | | | | 7 5 | C | + | | | 7 5 | D | + | | | 14 5 | E | + | | | 7 5 | G | = | | 7 | (16) | , then add the two sides of equation (16) to both sides of equation (4), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | | | 24 5 | C | | -2 | D | | - | 7 5 | E | | - | 13 5 | F | + | | | 6 5 | G | = | | - | 11 5 | | (5) |
| | - | 14 5 | C | + | | 3 | D | + | | | 2 5 | E | + | | | 3 5 | F | + | | | 19 5 | G | = | | - | 4 5 | | (6) |
| | - | 26 5 | C | | -3 | D | + | | | 18 5 | E | + | | | 27 5 | F | | - | 9 5 | G | = | | - | 1 5 | | (7) |
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Multiply both sides of equation (3) by 24 Divide the two sides of equation (3) by 5, the equation can be obtained: | | | | 24 5 | C | + | | | 24 5 | D | + | | | 48 5 | E | + | | | 24 5 | G | = | | 24 | (17) | , then subtract both sides of equation (17) from both sides of equation (5), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | - | 34 5 | D | | -11 | E | | - | 13 5 | F | | - | 18 5 | G | = | | - | 131 5 | | (5) |
| | - | 14 5 | C | + | | 3 | D | + | | | 2 5 | E | + | | | 3 5 | F | + | | | 19 5 | G | = | | - | 4 5 | | (6) |
| | - | 26 5 | C | | -3 | D | + | | | 18 5 | E | + | | | 27 5 | F | | - | 9 5 | G | = | | - | 1 5 | | (7) |
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Multiply both sides of equation (3) by 14 Divide the two sides of equation (3) by 5, the equation can be obtained: | | | | 14 5 | C | + | | | 14 5 | D | + | | | 28 5 | E | + | | | 14 5 | G | = | | 14 | (18) | , then add the two sides of equation (18) to both sides of equation (6), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | - | 34 5 | D | | -11 | E | | - | 13 5 | F | | - | 18 5 | G | = | | - | 131 5 | | (5) |
| | | | 29 5 | D | + | | 6 | E | + | | | 3 5 | F | + | | | 33 5 | G | = | | | 66 5 | | (6) |
| | - | 26 5 | C | | -3 | D | + | | | 18 5 | E | + | | | 27 5 | F | | - | 9 5 | G | = | | - | 1 5 | | (7) |
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Multiply both sides of equation (3) by 26 Divide the two sides of equation (3) by 5, the equation can be obtained: | | | | 26 5 | C | + | | | 26 5 | D | + | | | 52 5 | E | + | | | 26 5 | G | = | | 26 | (19) | , then add the two sides of equation (19) to both sides of equation (7), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | - | 34 5 | D | | -11 | E | | - | 13 5 | F | | - | 18 5 | G | = | | - | 131 5 | | (5) |
| | | | 29 5 | D | + | | 6 | E | + | | | 3 5 | F | + | | | 33 5 | G | = | | | 66 5 | | (6) |
| | | | 11 5 | D | + | | 14 | E | + | | | 27 5 | F | + | | | 17 5 | G | = | | | 129 5 | | (7) |
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Multiply both sides of equation (4) by 17 Divide the two sides of equation (4) by 6, the equation can be obtained: | | | | 34 5 | D | + | | 17 | E | | - | 17 30 | F | | - | 136 15 | G | = | | | 323 15 | (20) | , then add the two sides of equation (20) to both sides of equation (5), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | | 6 | E | | - | 19 6 | F | | - | 38 3 | G | = | | - | 14 3 | | (5) |
| | | | 29 5 | D | + | | 6 | E | + | | | 3 5 | F | + | | | 33 5 | G | = | | | 66 5 | | (6) |
| | | | 11 5 | D | + | | 14 | E | + | | | 27 5 | F | + | | | 17 5 | G | = | | | 129 5 | | (7) |
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Multiply both sides of equation (4) by 29 Divide the two sides of equation (4) by 12, the equation can be obtained: | | | | 29 5 | D | + | | | 29 2 | E | | - | 29 60 | F | | - | 116 15 | G | = | | | 551 30 | (21) | , then subtract both sides of equation (21) from both sides of equation (6), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | | 6 | E | | - | 19 6 | F | | - | 38 3 | G | = | | - | 14 3 | | (5) |
| | - | 17 2 | E | + | | | 13 12 | F | + | | | 43 3 | G | = | | - | 31 6 | | (6) |
| | | | 11 5 | D | + | | 14 | E | + | | | 27 5 | F | + | | | 17 5 | G | = | | | 129 5 | | (7) |
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Multiply both sides of equation (4) by 11 Divide the two sides of equation (4) by 12, the equation can be obtained: | | | | 11 5 | D | + | | | 11 2 | E | | - | 11 60 | F | | - | 44 15 | G | = | | | 209 30 | (22) | , then subtract both sides of equation (22) from both sides of equation (7), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | | 6 | E | | - | 19 6 | F | | - | 38 3 | G | = | | - | 14 3 | | (5) |
| | - | 17 2 | E | + | | | 13 12 | F | + | | | 43 3 | G | = | | - | 31 6 | | (6) |
| | | | 17 2 | E | + | | | 67 12 | F | + | | | 19 3 | G | = | | | 113 6 | | (7) |
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Multiply both sides of equation (5) by 17 Divide the two sides of equation (5) by 12, the equation can be obtained: | | | | 17 2 | E | | - | 323 72 | F | | - | 323 18 | G | = | | - | 119 18 | (23) | , then add the two sides of equation (23) to both sides of equation (6), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | | 6 | E | | - | 19 6 | F | | - | 38 3 | G | = | | - | 14 3 | | (5) |
| | - | 245 72 | F | | - | 65 18 | G | = | | - | 106 9 | | (6) |
| | | | 17 2 | E | + | | | 67 12 | F | + | | | 19 3 | G | = | | | 113 6 | | (7) |
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Multiply both sides of equation (5) by 17 Divide the two sides of equation (5) by 12, the equation can be obtained: | | | | 17 2 | E | | - | 323 72 | F | | - | 323 18 | G | = | | - | 119 18 | (24) | , then subtract both sides of equation (24) from both sides of equation (7), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | | 6 | E | | - | 19 6 | F | | - | 38 3 | G | = | | - | 14 3 | | (5) |
| | - | 245 72 | F | | - | 65 18 | G | = | | - | 106 9 | | (6) |
| | | | 725 72 | F | + | | | 437 18 | G | = | | | 229 9 | | (7) |
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Multiply both sides of equation (6) by 145 Divide the two sides of equation (6) by 49, the equation can be obtained: | | - | 725 72 | F | | - | 9425 882 | G | = | | - | 15370 441 | (25) | , then add the two sides of equation (25) to both sides of equation (7), the equations are reduced to:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | | 6 | E | | - | 19 6 | F | | - | 38 3 | G | = | | - | 14 3 | | (5) |
| | - | 245 72 | F | | - | 65 18 | G | = | | - | 106 9 | | (6) |
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Multiply both sides of equation (7) by 3185 Divide both sides of equation (7) by 11988, get the equation:| | | | 65 18 | G | = | | - | 29965 11988 | (26) | , then add the two sides of equation (26) to both sides of equation (6), get the equation:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | | 6 | E | | - | 19 6 | F | | - | 38 3 | G | = | | - | 14 3 | | (5) |
| | - | 245 72 | F | = | | - | 171157 11988 | | (6) |
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Multiply both sides of equation (7) by 931 Divide both sides of equation (7) by 999, get the equation:, then add the two sides of equation (27) to both sides of equation (5), get the equation:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | | - | 16 5 | G | = | | | 38 5 | | (4) |
| | | 6 | E | | - | 19 6 | F | = | | - | 13421 999 | | (5) |
| | - | 245 72 | F | = | | - | 171157 11988 | | (6) |
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Multiply both sides of equation (7) by 392 Divide both sides of equation (7) by 1665, get the equation:, then add the two sides of equation (28) to both sides of equation (4), get the equation:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | = | | | 8966 1665 | | (4) |
| | | 6 | E | | - | 19 6 | F | = | | - | 13421 999 | | (5) |
| | - | 245 72 | F | = | | - | 171157 11988 | | (6) |
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Multiply both sides of equation (7) by 49 Divide both sides of equation (7) by 666, get the equation:, then subtract both sides of equation (29) from both sides of equation (3), get the equation:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | + | | 2 | G | = | | 8 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | = | | | 8966 1665 | | (4) |
| | | 6 | E | | - | 19 6 | F | = | | - | 13421 999 | | (5) |
| | - | 245 72 | F | = | | - | 171157 11988 | | (6) |
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Multiply both sides of equation (7) by 49 Divide both sides of equation (7) by 333, get the equation:, then subtract both sides of equation (30) from both sides of equation (2), get the equation:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | | -2 | G | = | | -4 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | = | | | 3125 333 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | = | | | 8966 1665 | | (4) |
| | | 6 | E | | - | 19 6 | F | = | | - | 13421 999 | | (5) |
| | - | 245 72 | F | = | | - | 171157 11988 | | (6) |
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Multiply both sides of equation (7) by 49 Divide both sides of equation (7) by 333, get the equation:, then add the two sides of equation (31) to both sides of equation (1), get the equation:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | = | | - | 1793 333 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | = | | | 3125 333 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | = | | | 8966 1665 | | (4) |
| | | 6 | E | | - | 19 6 | F | = | | - | 13421 999 | | (5) |
| | - | 245 72 | F | = | | - | 171157 11988 | | (6) |
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Multiply both sides of equation (6) by 228 Divide both sides of equation (6) by 245, get the equation:| | - | 19 6 | F | = | | - | 66367 4995 | (32) | , then subtract both sides of equation (32) from both sides of equation (5), get the equation:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | = | | - | 1793 333 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | = | | | 3125 333 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | | - | 1 5 | F | = | | | 8966 1665 | | (4) |
| | | - | 245 72 | F | = | | - | 171157 11988 | | (6) |
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Multiply both sides of equation (6) by 72 Divide both sides of equation (6) by 1225, get the equation:, then subtract both sides of equation (33) from both sides of equation (4), get the equation:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | = | | - | 1793 333 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | | -1 | F | = | | | 3125 333 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | = | | | 17272 2775 | | (4) |
| | | - | 245 72 | F | = | | - | 171157 11988 | | (6) |
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Multiply both sides of equation (6) by 72 Divide both sides of equation (6) by 245, get the equation:, then subtract both sides of equation (34) from both sides of equation (2), get the equation:
 | | | | | A | | -2 | B | | -3 | E | + | | 2 | F | = | | - | 1793 333 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | = | | | 7537 555 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | = | | | 17272 2775 | | (4) |
| | | - | 245 72 | F | = | | - | 171157 11988 | | (6) |
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Multiply both sides of equation (6) by 144 Divide both sides of equation (6) by 245, get the equation:, then add the two sides of equation (35) to both sides of equation (1), get the equation:
 | | | | | A | | -2 | B | | -3 | E | = | | - | 22937 1665 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | = | | | 7537 555 | | (2) |
| | | | | 12 5 | D | + | | 6 | E | = | | | 17272 2775 | | (4) |
| | | - | 245 72 | F | = | | - | 171157 11988 | | (6) |
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Subtract both sides of equation (5) from both sides of equation (4), get the equation:
 | | | | | A | | -2 | B | | -3 | E | = | | - | 22937 1665 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | = | | | 7537 555 | | (2) |
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Divide both sides of equation (5) by 3, get the equation:, then subtract both sides of equation (36) from both sides of equation (3), get the equation:
 | | | | | A | | -2 | B | | -3 | E | = | | - | 22937 1665 | | (1) |
| | | 5 | B | | -2 | C | + | | 6 | E | = | | | 7537 555 | | (2) |
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Subtract both sides of equation (5) from both sides of equation (2), get the equation:
 | | | | | A | | -2 | B | | -3 | E | = | | - | 22937 1665 | | (1) |
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Divide both sides of equation (5) by 2, get the equation:, then add the two sides of equation (37) to both sides of equation (1), get the equation:
Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 12, get the equation:, then subtract both sides of equation (38) from both sides of equation (3), get the equation:
Multiply both sides of equation (3) by 2, get the equation:, then add the two sides of equation (39) to both sides of equation (2), get the equation:
Multiply both sides of equation (2) by 2 Divide both sides of equation (2) by 5, get the equation:, then add the two sides of equation (40) 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》 |