detailed information: The input equation set is:
| | | | | | A | + | | 3 | B | + | | 9 | C | + | | 27 | D | = | | 18 | | (3) |
| | A | + | | 4 | B | + | | 16 | C | + | | 64 | D | = | | 52 | | (4) |
| Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | | | A | + | | 3 | B | + | | 9 | C | + | | 27 | D | = | | 18 | | (3) |
| | A | + | | 4 | B | + | | 16 | C | + | | 64 | D | = | | 52 | | (4) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | | | | A | + | | 4 | B | + | | 16 | C | + | | 64 | D | = | | 52 | | (4) |
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Subtract both sides of equation (1) from both sides of equation (4) ,the equations are reduced to:
Multiply both sides of equation (2) by 2, the equation can be obtained: , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 3, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (3) by 3, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (8) from both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 6, get the equation:, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
Divide both sides of equation (4) by 6, get the equation:, then subtract both sides of equation (10) 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 (11) from both sides of equation (2), get the equation:
Divide both sides of equation (3) by 2, get the equation:, then subtract both sides of equation (12) from both sides of equation (1), get the equation:
Subtract both sides of equation (2) 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:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |