detailed information: The input equation set is:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | | | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | 3 | A | | -2 | B | + | | C | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 0 | | (7) |
| | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| -6 | A | + | | 2 | B | + | | 6 | E | | -2 | F | = | | 0 | | (9) |
| | | | Question solving process:
Divide the two sides of equation (1) by 8, the equation can be obtained: | -1 | A | + | | | 1 2 | B | | - | 1 4 | C | + | | | 1 8 | D | = | | - | 1 2 | (13) | , then subtract both sides of equation (13) from both sides of equation (2), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | | | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | 3 | A | | -2 | B | + | | C | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 0 | | (7) |
| | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| -6 | A | + | | 2 | B | + | | 6 | E | | -2 | F | = | | 0 | | (9) |
| | | |
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 8, the equation can be obtained: | -3 | A | + | | | 3 2 | B | | - | 3 4 | C | + | | | 3 8 | D | = | | - | 3 2 | (14) | , then add the two sides of equation (14) to both sides of equation (7), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | | | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| - | 1 2 | B | + | | | 1 4 | C | + | | | 3 8 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | - | 3 2 | | (7) |
| | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| -6 | A | + | | 2 | B | + | | 6 | E | | -2 | F | = | | 0 | | (9) |
| | | |
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 4, the equation can be obtained: | -6 | A | + | | 3 | B | | - | 3 2 | C | + | | | 3 4 | D | = | | -3 | (15) | , then subtract both sides of equation (15) from both sides of equation (9), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | | | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| - | 1 2 | B | + | | | 1 4 | C | + | | | 3 8 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | - | 3 2 | | (7) |
| | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| -1 | B | + | | | 3 2 | C | | - | 3 4 | D | + | | 6 | E | | -2 | F | = | | 3 | | (9) |
| | | |
Multiply both sides of equation (1) by 3 Divide the two sides of equation (1) by 2, the equation can be obtained: | -12 | A | + | | 6 | B | | -3 | C | + | | | 3 2 | D | = | | -6 | (16) | , then subtract both sides of equation (16) from both sides of equation (11), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | | | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| - | 1 2 | B | + | | | 1 4 | C | + | | | 3 8 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | - | 3 2 | | (7) |
| | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| -1 | B | + | | | 3 2 | C | | - | 3 4 | D | + | | 6 | E | | -2 | F | = | | 3 | | (9) |
| | | |
Add both sides of equation (2) to both sides of equation (7) ,the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | | | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (7) |
| | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| -1 | B | + | | | 3 2 | C | | - | 3 4 | D | + | | 6 | E | | -2 | F | = | | 3 | | (9) |
| | | |
Multiply both sides of equation (2) by 2, the equation can be obtained: , then add the two sides of equation (17) to both sides of equation (9), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | | | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (7) |
| | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| | | | |
Multiply both sides of equation (2) by 8, the equation can be obtained: , then add the two sides of equation (18) to both sides of equation (11), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | | | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (7) |
| | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| | | | |
交After the exchange of equation (3) and equation (7), the equation system becomes:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| | | | |
Multiply both sides of equation (3) by 6, the equation can be obtained: | -3 | C | + | | | 15 2 | D | | -18 | E | + | | 12 | F | | -6 | G | + | | 24 | J | = | | 12 | (19) | , then subtract both sides of equation (19) from both sides of equation (11), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| | | -2 | D | + | | 18 | E | | -12 | F | + | | 6 | G | | -24 | J | = | | 22 | | (11) |
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交After the exchange of equation (4) and equation (9), the equation system becomes:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| | | -2 | D | + | | 18 | E | | -12 | F | + | | 6 | G | | -24 | J | = | | 22 | | (11) |
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Multiply both sides of equation (4) by 2, the equation can be obtained: , then add the two sides of equation (20) to both sides of equation (11), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| | | | 30 | E | | -16 | F | + | | 6 | G | | -24 | J | = | | 42 | | (11) |
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交After the exchange of equation (5) and equation (7), the equation system becomes:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | | 3 | E | + | | 2 | F | + | | G | | -3 | I | | -2 | J | | -1 | K | = | | 0 | | (8) |
| | | | 30 | E | | -16 | F | + | | 6 | G | | -24 | J | = | | 42 | | (11) |
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Multiply both sides of equation (5) by 3, the equation can be obtained: | -3 | E | + | | 3 | F | | -3 | G | + | | 3 | H | = | | 9 | (21) | , then add the two sides of equation (21) to both sides of equation (8), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (8) |
| | | | 30 | E | | -16 | F | + | | 6 | G | | -24 | J | = | | 42 | | (11) |
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Add both sides of equation (5) to both sides of equation (9) ,the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (8) |
| | | | 30 | E | | -16 | F | + | | 6 | G | | -24 | J | = | | 42 | | (11) |
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Multiply both sides of equation (5) by 6, the equation can be obtained: | -6 | E | + | | 6 | F | | -6 | G | + | | 6 | H | = | | 18 | (22) | , then add the two sides of equation (22) to both sides of equation (10), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (8) |
| | | 8 | F | | -6 | G | + | | 6 | H | | -6 | I | | -2 | J | = | | 18 | | (10) |
| | 30 | E | | -16 | F | + | | 6 | G | | -24 | J | = | | 42 | | (11) |
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Multiply both sides of equation (5) by 30, the equation can be obtained: | -30 | E | + | | 30 | F | | -30 | G | + | | 30 | H | = | | 90 | (23) | , then add the two sides of equation (23) to both sides of equation (11), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (6) |
| | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (8) |
| | | 8 | F | | -6 | G | + | | 6 | H | | -6 | I | | -2 | J | = | | 18 | | (10) |
| | 14 | F | | -24 | G | + | | 30 | H | | -24 | J | = | | 132 | | (11) |
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交After the exchange of equation (6) and equation (8), the equation system becomes:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (8) |
| | | 8 | F | | -6 | G | + | | 6 | H | | -6 | I | | -2 | J | = | | 18 | | (10) |
| | 14 | F | | -24 | G | + | | 30 | H | | -24 | J | = | | 132 | | (11) |
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Multiply both sides of equation (6) by 2 Divide the two sides of equation (6) by 5, the equation can be obtained: | | 2 | F | | - | 4 5 | G | + | | | 6 5 | H | | - | 6 5 | I | | - | 4 5 | J | | - | 2 5 | K | = | | | 18 5 | (24) | , then subtract both sides of equation (24) from both sides of equation (9), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (8) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (9) |
| | 8 | F | | -6 | G | + | | 6 | H | | -6 | I | | -2 | J | = | | 18 | | (10) |
| | 14 | F | | -24 | G | + | | 30 | H | | -24 | J | = | | 132 | | (11) |
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Multiply both sides of equation (6) by 8 Divide the two sides of equation (6) by 5, the equation can be obtained: | | 8 | F | | - | 16 5 | G | + | | | 24 5 | H | | - | 24 5 | I | | - | 16 5 | J | | - | 8 5 | K | = | | | 72 5 | (25) | , then subtract both sides of equation (25) from both sides of equation (10), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (8) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (9) |
| - | 14 5 | G | + | | | 6 5 | H | | - | 6 5 | I | + | | | 6 5 | J | + | | | 8 5 | K | = | | | 18 5 | | (10) |
| | 14 | F | | -24 | G | + | | 30 | H | | -24 | J | = | | 132 | | (11) |
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Multiply both sides of equation (6) by 14 Divide the two sides of equation (6) by 5, the equation can be obtained: | | 14 | F | | - | 28 5 | G | + | | | 42 5 | H | | - | 42 5 | I | | - | 28 5 | J | | - | 14 5 | K | = | | | 126 5 | (26) | , then subtract both sides of equation (26) from both sides of equation (11), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (8) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (9) |
| - | 14 5 | G | + | | | 6 5 | H | | - | 6 5 | I | + | | | 6 5 | J | + | | | 8 5 | K | = | | | 18 5 | | (10) |
| - | 92 5 | G | + | | | 108 5 | H | + | | | 42 5 | I | | - | 92 5 | J | + | | | 14 5 | K | = | | | 534 5 | | (11) |
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交After the exchange of equation (7) and equation (9), the equation system becomes:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (8) |
| | - | 14 5 | G | + | | | 6 5 | H | | - | 6 5 | I | + | | | 6 5 | J | + | | | 8 5 | K | = | | | 18 5 | | (10) |
| - | 92 5 | G | + | | | 108 5 | H | + | | | 42 5 | I | | - | 92 5 | J | + | | | 14 5 | K | = | | | 534 5 | | (11) |
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Multiply both sides of equation (7) by 7 Divide the two sides of equation (7) by 2, the equation can be obtained: | | | 14 5 | G | + | | | 14 5 | H | + | | | 21 5 | I | + | | | 14 5 | J | + | | | 7 5 | K | = | | | 77 5 | (27) | , then add the two sides of equation (27) to both sides of equation (10), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (8) |
| | | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (10) |
| - | 92 5 | G | + | | | 108 5 | H | + | | | 42 5 | I | | - | 92 5 | J | + | | | 14 5 | K | = | | | 534 5 | | (11) |
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Multiply both sides of equation (7) by 23, the equation can be obtained: | | | 92 5 | G | + | | | 92 5 | H | + | | | 138 5 | I | + | | | 92 5 | J | + | | | 46 5 | K | = | | | 506 5 | (28) | , then add the two sides of equation (28) to both sides of equation (11), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (8) |
| | | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (10) |
| | 40 | H | + | | 36 | I | + | | 12 | K | = | | 208 | | (11) |
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交After the exchange of equation (8) and equation (10), the equation system becomes:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
| | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (10) |
| | 40 | H | + | | 36 | I | + | | 12 | K | = | | 208 | | (11) |
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Multiply both sides of equation (8) by 10, the equation can be obtained: | | 40 | H | + | | 30 | I | + | | 40 | J | + | | 30 | K | = | | 190 | (29) | , then subtract both sides of equation (29) from both sides of equation (11), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
| | | 8 | I | + | | 4 | J | + | | 2 | K | + | | L | = | | 12 | | (10) |
| | |
Multiply both sides of equation (9) by 8, the equation can be obtained: | | 8 | I | + | | 8 | J | + | | 8 | K | + | | 8 | L | = | | 40 | (30) | , then subtract both sides of equation (30) from both sides of equation (10), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
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Multiply both sides of equation (9) by 6, the equation can be obtained: | | 6 | I | + | | 6 | J | + | | 6 | K | + | | 6 | L | = | | 30 | (31) | , then subtract both sides of equation (31) from both sides of equation (11), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
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Multiply both sides of equation (9) by 12, the equation can be obtained: | | 12 | I | + | | 12 | J | + | | 12 | K | + | | 12 | L | = | | 60 | (32) | , then subtract both sides of equation (32) from both sides of equation (12), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
| | | | -10 | J | | -12 | K | | -12 | L | = | | -60 | | (12) |
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Multiply both sides of equation (10) by 23 Divide the two sides of equation (10) by 2, the equation can be obtained: | -46 | J | | -69 | K | | - | 161 2 | L | = | | -322 | (33) | , then subtract both sides of equation (33) from both sides of equation (11), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
| | | | -10 | J | | -12 | K | | -12 | L | = | | -60 | | (12) |
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Multiply both sides of equation (10) by 5 Divide the two sides of equation (10) by 2, the equation can be obtained: | -10 | J | | -15 | K | | - | 35 2 | L | = | | -70 | (34) | , then subtract both sides of equation (34) from both sides of equation (12), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
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Divide the two sides of equation (11) by 15, the equation can be obtained: , then subtract both sides of equation (35) from both sides of equation (12), the equations are reduced to:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
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Multiply both sides of equation (12) by 2235 Divide both sides of equation (12) by 16, get the equation:, then subtract both sides of equation (36) from both sides of equation (11), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
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Multiply both sides of equation (12) by 105 Divide both sides of equation (12) by 8, get the equation:, then add the two sides of equation (37) to both sides of equation (10), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
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Multiply both sides of equation (12) by 15 Divide both sides of equation (12) by 8, get the equation:, then subtract both sides of equation (38) from both sides of equation (9), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
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Multiply both sides of equation (11) by 2 Divide both sides of equation (11) by 15, get the equation:, then add the two sides of equation (39) to both sides of equation (10), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
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Divide both sides of equation (11) by 45, get the equation:, then subtract both sides of equation (40) from both sides of equation (9), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
| | 4 | H | + | | 3 | I | + | | 4 | J | + | | 3 | K | = | | 19 | | (8) |
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Divide both sides of equation (11) by 15, get the equation:, then subtract both sides of equation (41) from both sides of equation (8), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | + | | | 2 5 | K | = | | | 22 5 | | (7) |
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Multiply both sides of equation (11) by 2 Divide both sides of equation (11) by 225, get the equation:, then subtract both sides of equation (42) from both sides of equation (7), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | | -1 | K | = | | 9 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | = | | - | 58 5 | | (7) |
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Divide both sides of equation (11) by 45, get the equation:, then add the two sides of equation (43) to both sides of equation (6), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | = | | 49 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | = | | - | 58 5 | | (7) |
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Divide both sides of equation (10) by 4, get the equation:, then add the two sides of equation (44) to both sides of equation (9), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | = | | 49 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | = | | - | 58 5 | | (7) |
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Add both sides of equation (10) to both sides of equation (8), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | = | | 49 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | + | | | 4 5 | J | = | | - | 58 5 | | (7) |
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Divide both sides of equation (10) by 5, get the equation:, then add the two sides of equation (45) to both sides of equation (7), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | 5 | F | | -2 | G | + | | 3 | H | | -3 | I | | -2 | J | = | | 49 | | (6) |
| | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | = | | | 14 5 | | (7) |
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Divide both sides of equation (10) by 2, get the equation:, then subtract both sides of equation (46) from both sides of equation (6), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | + | | 4 | J | = | | 2 | | (3) |
| | | | | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | = | | | 14 5 | | (7) |
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Add both sides of equation (10) to both sides of equation (3), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | = | | 74 | | (3) |
| | | | | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | = | | | 14 5 | | (7) |
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Multiply both sides of equation (9) by 3, get the equation:, then subtract both sides of equation (47) from both sides of equation (8), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | = | | 74 | | (3) |
| | | | | | 4 5 | G | + | | | 4 5 | H | + | | | 6 5 | I | = | | | 14 5 | | (7) |
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Multiply both sides of equation (9) by 6 Divide both sides of equation (9) by 5, get the equation:, then subtract both sides of equation (48) from both sides of equation (7), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | = | | 74 | | (3) |
| | | | | | | | | |
Multiply both sides of equation (9) by 3, get the equation:, then add the two sides of equation (49) to both sides of equation (6), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | = | | 74 | | (3) |
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Divide both sides of equation (8) by 5, get the equation:, then subtract both sides of equation (50) from both sides of equation (7), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | = | | 74 | | (3) |
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Multiply both sides of equation (8) by 3 Divide both sides of equation (8) by 4, get the equation:, then subtract both sides of equation (51) from both sides of equation (6), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | = | | 74 | | (3) |
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Divide both sides of equation (8) by 4, get the equation:, then subtract both sides of equation (52) from both sides of equation (5), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | = | | 74 | | (3) |
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Multiply both sides of equation (7) by 5 Divide both sides of equation (7) by 2, get the equation:, then add the two sides of equation (53) to both sides of equation (6), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | = | | 74 | | (3) |
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Multiply both sides of equation (7) by 5 Divide both sides of equation (7) by 4, get the equation:, then add the two sides of equation (54) to both sides of equation (5), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | | -1 | G | = | | 74 | | (3) |
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Multiply both sides of equation (7) by 5 Divide both sides of equation (7) by 4, get the equation:, then add the two sides of equation (55) to both sides of equation (3), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | = | | | 165 2 | | (3) |
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Divide both sides of equation (6) by 5, get the equation:, then subtract both sides of equation (56) from both sides of equation (5), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | = | | | 165 2 | | (3) |
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Multiply both sides of equation (6) by 2 Divide both sides of equation (6) by 5, get the equation:, then add the two sides of equation (57) to both sides of equation (4), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | + | | 2 | F | = | | | 165 2 | | (3) |
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Multiply both sides of equation (6) by 2 Divide both sides of equation (6) by 5, get the equation:, then subtract both sides of equation (58) from both sides of equation (3), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | = | | | 111 2 | | (3) |
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Multiply both sides of equation (5) by 6, get the equation:, then add the two sides of equation (59) to both sides of equation (4), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | - | 1 2 | C | + | | | 5 4 | D | | -3 | E | = | | | 111 2 | | (3) |
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Multiply both sides of equation (5) by 3, get the equation:, then subtract both sides of equation (60) from both sides of equation (3), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | | | | | | | | | | |
Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 4, get the equation:, then subtract both sides of equation (61) from both sides of equation (3), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
| | | | | | | | | | | |
Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 8, get the equation:, then subtract both sides of equation (62) from both sides of equation (2), get the equation:
| | | -8 | A | + | | 4 | B | | -2 | C | + | | D | = | | -4 | | (1) |
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Subtract both sides of equation (4) from both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 3 Divide both sides of equation (3) by 2, get the equation:, then subtract both sides of equation (63) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 4, get the equation:, then subtract both sides of equation (64) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 8, get the equation:, then subtract both sides of equation (65) from 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》 |