detailed information: The input equation set is:
 | | | | -4 | A | + | | 16 | B | | -12 | C | | -12 | D | = | | 0 | | (2) |
| | -12 | B | + | | 12 | C | + | | 15 | D | = | | 18 | | (4) |
| Question solving process:
Multiply both sides of equation (1) by 4 Divide the two sides of equation (1) by 7, the equation can be obtained: , then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 | | | | | | -12 | B | + | | 12 | C | + | | 15 | D | = | | 18 | | (4) |
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Multiply both sides of equation (2) by 7 Divide the two sides of equation (2) by 8, the equation can be obtained: | | 12 | B | | - | 21 2 | C | | - | 21 2 | D | = | | 9 | (6) | , then add the two sides of equation (6) to both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (3) by 3 Divide the two sides of equation (3) by 2, 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 8 Divide both sides of equation (4) by 3, get the equation:, then add the two sides of equation (8) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 12, get the equation:, then add the two sides of equation (9) to both sides of equation (2), get the equation:
Multiply both sides of equation (2) by 7 Divide both sides of equation (2) by 24, get the equation:, then add the two sides of equation (10) 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》 |