detailed information: The input equation set is:
| | | | | | 20 | A | + | | 4 | B | + | | 8 | C | + | | 4 | D | = | | 0 | | (3) |
| | Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | | | 20 | A | + | | 4 | B | + | | 8 | C | + | | 4 | D | = | | 0 | | (3) |
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Multiply both sides of equation (1) by 20, 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 (1) by 16, 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 (2) by 16 Divide the two sides of equation (2) by 3, the equation can be obtained: | | 16 | B | + | | | 80 3 | C | + | | | 16 3 | D | = | | 0 | (7) | , then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 16 Divide the two sides of equation (2) by 3, the equation can be obtained: | | 16 | B | + | | | 80 3 | C | + | | | 16 3 | D | = | | 0 | (8) | , then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (3) by 8 Divide the two sides of equation (3) by 11, the equation can be obtained: , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (4) by 77 Divide both sides of equation (4) by 12, get the equation:, then add the two sides of equation (10) to both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 11 Divide both sides of equation (4) by 16, get the equation:, then add the two sides of equation (11) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 15 Divide both sides of equation (3) by 44, get the equation:, then subtract both sides of equation (12) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 3 Divide both sides of equation (3) by 44, get the equation:, then subtract both sides of equation (13) from both sides of equation (1), get the equation:
Divide both sides of equation (2) by 3, get the equation:, then subtract both sides of equation (14) 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》 |