B4 Determine all pairs of positive integers $(x, y)$ that satisfy the equation

$$
3 x y-2 x-y=8 \text {. }
$$

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B4. Solutions of $3 x y-2 x-y=8$ are also solutions of $9 x y-6 x-3 y=24$ and we can write this as $9 x y-6 x-3 y+2=26$ or $(3 x-1)(3 y-2)=26$. Now, 26 can be written as $1 \times 26$ or $2 \times 13$. Now, $1 \times 26=(3-2)(27-1)$ and this gives the solution $(x, y)=(9,1)$. Further, $2 \times 13=(3-1)(15-2)$ and this gives $(x, y)=(1,5)$.

![](https://cdn.mathpix.com/cropped/2024_04_17_7fa3f9281a1c56596c60g-2.jpg?height=266&width=302&top_left_y=2460&top_left_x=1348)