detailed information: The input equation set is:
| | | | | | | 16 | A | + | | 16 | B | + | | 16 | C | + | | 60 | D | = | | 8443 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 4 Divide the two sides of equation (1) by 25, the equation can be obtained: | | 16 | A | + | | | 52 25 | D | = | | | 36324 25 | (5) | , then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
| | | | | | | 16 | B | + | | 16 | C | + | | | 1448 25 | D | = | | | 174751 25 | | (4) |
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Divide the two sides of equation (2) by 4, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
| | | | | | | 16 | C | + | | | 2771 50 | D | = | | | 515629 100 | | (4) |
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Multiply both sides of equation (3) by 4 Divide the two sides of equation (3) by 17, the equation can be obtained: | | 16 | C | + | | | 52 17 | D | = | | | 14668 17 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | | | | 44507 850 | D | = | | | 7298893 1700 | | (4) |
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Multiply both sides of equation (4) by 11050 Divide both sides of equation (4) by 44507, get the equation: | | | 578591 44507 | D | = | | | 94885609 89014 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), get the equation:
| | | | | | | | 44507 850 | D | = | | | 7298893 1700 | | (4) |
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Multiply both sides of equation (4) by 8500 Divide both sides of equation (4) by 44507, get the equation: | | | 445070 44507 | D | = | | | 36494465 44507 | (9) | , then subtract both sides of equation (9) from both sides of equation (2), get the equation:
| | | | | | | | 44507 850 | D | = | | | 7298893 1700 | | (4) |
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Multiply both sides of equation (4) by 11050 Divide both sides of equation (4) by 44507, get the equation: | | | 578591 44507 | D | = | | | 94885609 89014 | (10) | , then subtract both sides of equation (10) from both sides of equation (1), get the equation:
| | | | 100 | A | = | | | 713450525 89014 | | (1) |
| | | | | 44507 850 | D | = | | | 7298893 1700 | | (4) |
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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》 |