detailed information: The input equation set is: Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | | 1 2 | A | | - | 1 4 | C | | - | 1 4 | D | = | | -50 | (15) | , then add the two sides of equation (15) to both sides of equation (2), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
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Divide the two sides of equation (1) by 2, the equation can be obtained: | | | 1 2 | A | | - | 1 4 | C | | - | 1 4 | D | = | | -50 | (16) | , then add the two sides of equation (16) to both sides of equation (4), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | - | 1 4 | C | + | | | 3 4 | D | | - | 1 2 | G | = | | 0 | | (4) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: | | | 1 2 | B | | - | 1 8 | C | | - | 1 8 | D | | - | 1 4 | H | = | | -25 | (17) | , then add the two sides of equation (17) to both sides of equation (3), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| - | 1 4 | C | + | | | 3 4 | D | | - | 1 2 | G | = | | 0 | | (4) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: | | | 1 2 | B | | - | 1 8 | C | | - | 1 8 | D | | - | 1 4 | H | = | | -25 | (18) | , then add the two sides of equation (18) to both sides of equation (8), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| - | 1 4 | C | + | | | 3 4 | D | | - | 1 2 | G | = | | 0 | | (4) |
| | | | - | 1 8 | C | | - | 1 8 | D | | - | 1 2 | E | + | | | 3 4 | H | = | | -25 | | (8) |
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Multiply both sides of equation (3) by 2 Divide the two sides of equation (3) by 7, the equation can be obtained: | | | 1 4 | C | | - | 1 28 | D | | - | 1 7 | E | | - | 1 14 | H | = | | - | 50 7 | (19) | , then add the two sides of equation (19) to both sides of equation (4), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | | - | 1 8 | C | | - | 1 8 | D | | - | 1 2 | E | + | | | 3 4 | H | = | | -25 | | (8) |
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Multiply both sides of equation (3) by 4 Divide the two sides of equation (3) by 7, the equation can be obtained: | | | 1 2 | C | | - | 1 14 | D | | - | 2 7 | E | | - | 1 7 | H | = | | - | 100 7 | (20) | , then add the two sides of equation (20) to both sides of equation (5), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| - | 1 14 | D | + | | | 5 7 | E | | - | 1 2 | F | | - | 1 7 | H | = | | - | 100 7 | | (5) |
| | | - | 1 8 | C | | - | 1 8 | D | | - | 1 2 | E | + | | | 3 4 | H | = | | -25 | | (8) |
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Divide the two sides of equation (3) by 7, the equation can be obtained: | | | 1 8 | C | | - | 1 56 | D | | - | 1 14 | E | | - | 1 28 | H | = | | - | 25 7 | (21) | , then add the two sides of equation (21) to both sides of equation (8), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| - | 1 14 | D | + | | | 5 7 | E | | - | 1 2 | F | | - | 1 7 | H | = | | - | 100 7 | | (5) |
| | | - | 1 7 | D | | - | 4 7 | E | + | | | 5 7 | H | = | | - | 200 7 | | (8) |
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Divide the two sides of equation (4) by 10, the equation can be obtained: | | | 1 14 | D | | - | 1 70 | E | | - | 1 20 | G | | - | 1 140 | H | = | | - | 5 7 | (22) | , then add the two sides of equation (22) to both sides of equation (5), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | - | 1 7 | D | | - | 4 7 | E | + | | | 5 7 | H | = | | - | 200 7 | | (8) |
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Multiply both sides of equation (4) by 7 Divide the two sides of equation (4) by 10, the equation can be obtained: | | | 1 2 | D | | - | 1 10 | E | | - | 7 20 | G | | - | 1 20 | H | = | | -5 | (23) | , then add the two sides of equation (23) to both sides of equation (7), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | - | 1 10 | E | | - | 1 2 | F | + | | | 13 20 | G | | - | 1 20 | H | = | | -5 | | (7) |
| - | 1 7 | D | | - | 4 7 | E | + | | | 5 7 | H | = | | - | 200 7 | | (8) |
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Divide the two sides of equation (4) by 5, the equation can be obtained: | | | 1 7 | D | | - | 1 35 | E | | - | 1 10 | G | | - | 1 70 | H | = | | - | 10 7 | (24) | , then add the two sides of equation (24) to both sides of equation (8), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | - | 1 10 | E | | - | 1 2 | F | + | | | 13 20 | G | | - | 1 20 | H | = | | -5 | | (7) |
| - | 3 5 | E | | - | 1 10 | G | + | | | 7 10 | H | = | | -30 | | (8) |
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Divide the two sides of equation (5) by 7, the equation can be obtained: | | | 1 10 | E | | - | 1 14 | F | | - | 1 140 | G | | - | 3 140 | H | = | | - | 15 7 | (25) | , then add the two sides of equation (25) to both sides of equation (7), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | - | 4 7 | F | + | | | 9 14 | G | | - | 1 14 | H | = | | - | 50 7 | | (7) |
| - | 3 5 | E | | - | 1 10 | G | + | | | 7 10 | H | = | | -30 | | (8) |
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Multiply both sides of equation (5) by 6 Divide the two sides of equation (5) by 7, the equation can be obtained: | | | 3 5 | E | | - | 3 7 | F | | - | 3 70 | G | | - | 9 70 | H | = | | - | 90 7 | (26) | , then add the two sides of equation (26) to both sides of equation (8), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | - | 4 7 | F | + | | | 9 14 | G | | - | 1 14 | H | = | | - | 50 7 | | (7) |
| - | 3 7 | F | | - | 1 7 | G | + | | | 4 7 | H | = | | - | 300 7 | | (8) |
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Multiply both sides of equation (6) by 4 Divide the two sides of equation (6) by 7, the equation can be obtained: , then add the two sides of equation (27) to both sides of equation (7), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
| - | 3 7 | F | | - | 1 7 | G | + | | | 4 7 | H | = | | - | 300 7 | | (8) |
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Multiply both sides of equation (6) by 3 Divide the two sides of equation (6) by 7, the equation can be obtained: | | | 3 7 | F | | - | 3 14 | G | | - | 3 14 | I | = | | 0 | (28) | , then add the two sides of equation (28) to both sides of equation (8), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
| - | 5 14 | G | + | | | 4 7 | H | | - | 3 14 | I | = | | - | 300 7 | | (8) |
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Add both sides of equation (7) to both sides of equation (8) ,the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Add both sides of equation (8) to both sides of equation (9) ,the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Add both sides of equation (9) to both sides of equation (10) ,the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Add both sides of equation (10) to both sides of equation (11) ,the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Add both sides of equation (11) to both sides of equation (12) ,the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Add both sides of equation (12) to both sides of equation (13) ,the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Multiply both sides of equation (13) by 2, the equation can be obtained: , then add the two sides of equation (29) to both sides of equation (14), the equations are reduced to:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Add both sides of equation (13) to both sides of equation (12), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Add both sides of equation (12) to both sides of equation (11), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Add both sides of equation (11) to both sides of equation (10), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Add both sides of equation (10) to both sides of equation (9), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Add both sides of equation (9) to both sides of equation (8), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | I | = | | - | 50 7 | | (7) |
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Multiply both sides of equation (9) by 4 Divide both sides of equation (9) by 7, get the equation:, then add the two sides of equation (30) to both sides of equation (7), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | N | = | | -150 | | (7) |
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Add both sides of equation (9) to both sides of equation (6), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 1 14 | H | | - | 2 7 | N | = | | -150 | | (7) |
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Divide both sides of equation (8) by 7, get the equation: | | | 1 14 | H | | - | 1 14 | N | = | | - | 300 7 | (31) | , then add the two sides of equation (31) to both sides of equation (7), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | H | = | | -15 | | (5) |
| | | | 5 14 | G | | - | 5 14 | N | = | | - | 1350 7 | | (7) |
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Multiply both sides of equation (8) by 3 Divide both sides of equation (8) by 10, get the equation:, then add the two sides of equation (32) to both sides of equation (5), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | H | = | | - | 50 7 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | N | = | | -105 | | (5) |
| | | | 5 14 | G | | - | 5 14 | N | = | | - | 1350 7 | | (7) |
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Divide both sides of equation (8) by 7, get the equation: | | | 1 14 | H | | - | 1 14 | N | = | | - | 300 7 | (33) | , then add the two sides of equation (33) to both sides of equation (4), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | H | = | | -25 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | N | = | | -50 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | N | = | | -105 | | (5) |
| | | | 5 14 | G | | - | 5 14 | N | = | | - | 1350 7 | | (7) |
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Divide both sides of equation (8) by 2, get the equation:, then add the two sides of equation (34) to both sides of equation (3), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | H | = | | -50 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | N | = | | -175 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | N | = | | -50 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | N | = | | -105 | | (5) |
| | | | 5 14 | G | | - | 5 14 | N | = | | - | 1350 7 | | (7) |
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Add both sides of equation (8) to both sides of equation (2), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | N | = | | -350 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | N | = | | -175 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | N | = | | -50 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | N | = | | -105 | | (5) |
| | | | 5 14 | G | | - | 5 14 | N | = | | - | 1350 7 | | (7) |
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Multiply both sides of equation (7) by 7 Divide both sides of equation (7) by 5, get the equation:, then add the two sides of equation (35) to both sides of equation (6), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | N | = | | -350 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | N | = | | -175 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | N | = | | -50 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 20 | G | | - | 3 20 | N | = | | -105 | | (5) |
| | | | 5 14 | G | | - | 5 14 | N | = | | - | 1350 7 | | (7) |
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Multiply both sides of equation (7) by 7 Divide both sides of equation (7) by 50, get the equation:, then add the two sides of equation (36) to both sides of equation (5), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | N | = | | -350 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | N | = | | -175 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 1 2 | G | | - | 1 14 | N | = | | -50 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 5 | N | = | | -132 | | (5) |
| | | | 5 14 | G | | - | 5 14 | N | = | | - | 1350 7 | | (7) |
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Multiply both sides of equation (7) by 7 Divide both sides of equation (7) by 5, get the equation:, then add the two sides of equation (37) to both sides of equation (4), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | N | = | | -350 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | N | = | | -175 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 4 7 | N | = | | -320 | | (4) |
| | | 7 10 | E | | - | 1 2 | F | | - | 1 5 | N | = | | -132 | | (5) |
| | | | 5 14 | G | | - | 5 14 | N | = | | - | 1350 7 | | (7) |
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Divide both sides of equation (6) by 2, get the equation:, then add the two sides of equation (38) to both sides of equation (5), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | N | = | | -350 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | N | = | | -175 | | (3) |
| | | 5 7 | D | | - | 1 7 | E | | - | 4 7 | N | = | | -320 | | (4) |
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Multiply both sides of equation (5) by 10 Divide both sides of equation (5) by 49, get the equation:, then add the two sides of equation (39) to both sides of equation (4), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | N | = | | -350 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 1 2 | E | | - | 1 4 | N | = | | -175 | | (3) |
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Multiply both sides of equation (5) by 5 Divide both sides of equation (5) by 7, get the equation:, then add the two sides of equation (40) to both sides of equation (3), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | N | = | | -350 | | (2) |
| | | 7 8 | C | | - | 1 8 | D | | - | 3 4 | N | = | | -455 | | (3) |
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Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 40, get the equation:, then add the two sides of equation (41) to both sides of equation (3), get the equation:
| | | | | B | | - | 1 4 | C | | - | 1 4 | D | | - | 1 2 | N | = | | -350 | | (2) |
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Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 20, get the equation:, then add the two sides of equation (42) to both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 10, get the equation:, then add the two sides of equation (43) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 7, get the equation:, then add the two sides of equation (44) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 4 Divide both sides of equation (3) by 7, get the equation:, then add the two sides of equation (45) 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:
Where: N 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》 |