detailed information: The input equation set is:
| | | | | | | 16 | A | + | | 16 | B | + | | 16 | C | + | | 60 | D | = | | 8000 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 8 Divide the two sides of equation (1) by 35, the equation can be obtained: , then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
| | | | | | | 16 | B | + | | 16 | C | + | | | 2028 35 | D | = | | | 270832 35 | | (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 | + | | | 3881 70 | D | = | | | 224807 35 | | (4) |
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Multiply both sides of equation (3) by 16 Divide the two sides of equation (3) by 61, the equation can be obtained: | | 16 | C | + | | | 192 61 | D | = | | | 71200 61 | (7) | , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | | | | 223301 4270 | D | = | | | 11221227 2135 | | (4) |
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Multiply both sides of equation (4) by 51240 Divide both sides of equation (4) by 223301, get the equation: | | | 2316 193 | D | = | | | 269309448 223301 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), get the equation:
| | | | | | 61 | C | = | | | 724380002 223301 | | (3) |
| | | 223301 4270 | D | = | | | 11221227 2135 | | (4) |
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Multiply both sides of equation (4) by 42700 Divide both sides of equation (4) by 223301, get the equation: | | | 1930 193 | D | = | | | 224424540 223301 | (9) | , then subtract both sides of equation (9) from both sides of equation (2), get the equation:
| | | | | 64 | B | = | | | 950138720 223301 | | (2) |
| | 61 | C | = | | | 724380002 223301 | | (3) |
| | | 223301 4270 | D | = | | | 11221227 2135 | | (4) |
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Multiply both sides of equation (4) by 38430 Divide both sides of equation (4) by 223301, get the equation: | | | 1737 193 | D | = | | | 201982086 223301 | (10) | , then subtract both sides of equation (10) from both sides of equation (1), get the equation:
| | | | | 64 | B | = | | | 950138720 223301 | | (2) |
| | 61 | C | = | | | 724380002 223301 | | (3) |
| | | 223301 4270 | D | = | | | 11221227 2135 | | (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》 |