detailed information: The input equation set is:
| | | | | A | + | | 9 | B | + | | 7 | C | + | | 14 | D | = | | 76 | | (2) |
| | A | + | | 2 | B | + | | 5 | C | + | | 9 | D | = | | 12 | | (3) |
| | 3 | A | + | | 6 | B | + | | 16 | C | + | | 26 | D | = | | 26 | | (4) |
| Question solving process:
Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
| | | | | | A | + | | 2 | B | + | | 5 | C | + | | 9 | D | = | | 12 | | (3) |
| | 3 | A | + | | 6 | B | + | | 16 | C | + | | 26 | D | = | | 26 | | (4) |
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Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
| | | | | | | 3 | A | + | | 6 | B | + | | 16 | C | + | | 26 | D | = | | 26 | | (4) |
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Multiply both sides of equation (1) by 3, the equation can be obtained: | | 3 | A | + | | 6 | B | + | | 18 | C | + | | 21 | D | = | | 0 | (5) | , then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
Multiply both sides of equation (3) by 2, 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 (4) by 2, get the equation:, then subtract both sides of equation (7) from both sides of equation (3), get the equation:
Multiply both sides of equation (4) by 7, get the equation:, then subtract both sides of equation (8) from both sides of equation (2), get the equation:
Multiply both sides of equation (4) by 7, get the equation:, then subtract both sides of equation (9) from both sides of equation (1), get the equation:
Add both sides of equation (3) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 6, get the equation:, then add the two sides of equation (10) to both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 2 Divide both sides of equation (2) by 7, get the equation:, then subtract both sides of equation (11) 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》 |