Bổ sung đề: Tìm x, y
\(a)3x+4y-xy=16\)
\(\Leftrightarrow3x-xy-12+4y=4\)
\(\Leftrightarrow x\left(3-y\right)-4\left(3-y\right)=4\)
\(\Leftrightarrow\left(x-4\right)\left(3-y\right)=4\)
\(\Leftrightarrow\left(x-4\right);\left(3-y\right)\inƯ\left(4\right)\)
Ta có: \(Ư\left(4\right)\in\left\{\pm1;\pm2\pm4\right\}\)
Lập bảng:
| x-4 | -1 | 1 | -2 | 2 | -4 | 4 |
| x | 3 | 5 | 2 | 6 | 0 | 8 |
| 3-y | -4 | 4 | -2 | 2 | -1 | 1 |
| y | 7 | -1 | 5 | 1 | 4 | 2 |
Vậy ...
\(b)xy+3x-2y=11\)
\(\Leftrightarrow x\left(y+3\right)-2y-6=5\)
\(\Leftrightarrow x\left(y+3\right)-2\left(y+3\right)=5\)
\(\Leftrightarrow\left(x-2\right)\left(y+3\right)=5\)
\(\Leftrightarrow\left(x-2\right);\left(y+3\right)\inƯ\left(5\right)\)
Ta có: \(Ư\left(5\right)\in\left\{\pm1;\pm5\right\}\)
Lập bảng:
| x-2 | -1 | 1 | -5 | 5 |
| x | 1 | 3 | -3 | 7 |
| y+3 | -5 | 5 | -1 | 1 |
| y | -8 | 2 | -4 | -2 |
Vậy ...