detailed information: The input equation set is:
| | | | A | + | | 17 | B | + | | 5 | C | + | | D | = | | 215 | | (1) |
| | 5 | A | + | | 22 | B | + | | 3 | C | + | | 4 | D | = | | 217 | | (2) |
| | 6 | A | + | | 24 | B | + | | 4 | C | + | | 5 | D | = | | 242 | | (3) |
| | 3 | A | + | | 27 | B | + | | 6 | C | + | | 2 | D | = | | 213 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 5, the equation can be obtained: | | 5 | A | + | | 85 | B | + | | 25 | C | + | | 5 | D | = | | 1075 | (5) | , then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
| | | | A | + | | 17 | B | + | | 5 | C | + | | D | = | | 215 | | (1) |
| | | 6 | A | + | | 24 | B | + | | 4 | C | + | | 5 | D | = | | 242 | | (3) |
| | 3 | A | + | | 27 | B | + | | 6 | C | + | | 2 | D | = | | 213 | | (4) |
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Multiply both sides of equation (1) by 6, the equation can be obtained: | | 6 | A | + | | 102 | B | + | | 30 | C | + | | 6 | D | = | | 1290 | (6) | , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | 17 | B | + | | 5 | C | + | | D | = | | 215 | | (1) |
| | -78 | B | | -26 | C | | -1 | D | = | | -1048 | | (3) |
| | 3 | A | + | | 27 | B | + | | 6 | C | + | | 2 | D | = | | 213 | | (4) |
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Multiply both sides of equation (1) by 3, the equation can be obtained: | | 3 | A | + | | 51 | B | + | | 15 | C | + | | 3 | D | = | | 645 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | 17 | B | + | | 5 | C | + | | D | = | | 215 | | (1) |
| | -78 | B | | -26 | C | | -1 | D | = | | -1048 | | (3) |
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Multiply both sides of equation (2) by 26 Divide the two sides of equation (2) by 21, the equation can be obtained: | -78 | B | | - | 572 21 | C | | - | 26 21 | D | = | | - | 7436 7 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | 17 | B | + | | 5 | C | + | | D | = | | 215 | | (1) |
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Multiply both sides of equation (2) by 8 Divide the two sides of equation (2) by 21, the equation can be obtained: | -24 | B | | - | 176 21 | C | | - | 8 21 | D | = | | - | 2288 7 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | 17 | B | + | | 5 | C | + | | D | = | | 215 | | (1) |
| | | - | 13 21 | C | | - | 13 21 | D | = | | - | 736 7 | | (4) |
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Divide the two sides of equation (3) by 2, the equation can be obtained: , then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
| | | | A | + | | 17 | B | + | | 5 | C | + | | D | = | | 215 | | (1) |
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Multiply both sides of equation (4) by 10 Divide both sides of equation (4) by 21, get the equation:, then add the two sides of equation (11) to both sides of equation (3), get the equation:
| | | | A | + | | 17 | B | + | | 5 | C | + | | D | = | | 215 | | (1) |
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Multiply both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (12) from both sides of equation (2), get the equation:
| | | | A | + | | 17 | B | + | | 5 | C | + | | D | = | | 215 | | (1) |
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Multiply both sides of equation (4) by 2, get the equation:, then add the two sides of equation (13) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 231 Divide both sides of equation (3) by 13, get the equation:, then add the two sides of equation (14) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 105 Divide both sides of equation (3) by 26, get the equation:, then subtract both sides of equation (15) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 17 Divide both sides of equation (2) by 63, get the equation:, then add the two sides of equation (16) 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》 |