Find the number of positive integers solutions of the equation $3x+2y=37$ where $x>0,y>0,\ \ x,y\in \mathbb{Z}$ .
By trial and error I found
$$\begin{array}{|c|c|} \hline x & y \\ \hline 11 & 2 \\ \hline 9 & 5 \\ \hline 7 & 8 \\ \hline 5 & 11 \\ \hline 3 & 14 \\ \hline 1 & 17 \\ \hline \end{array}$$
Total $\large 6$ pair of solutions. But i would like to know if their is a specific method to only find the number of positive solutions and not necessarily the actual solutions.
I look for a short and simple way. I have studied maths upto $12th$ grade.