Finding the integers modulo $n$ such that $x+y=2$, $2x-3y=3$ Determine the integers $n$ for which $\mathbb Z_n$, the set of integers modulo $n$, contains elements $x$ and $y$, such that $x+y=2$, $2x-3y=3$.
Some help will be much appreciated, thank you.

Hint $\rm\,\ \exists\, x,y\!:\,\begin{array}{r}\rm 2x-3y\equiv3\\ \rm x+y\equiv2\end{array}\!\iff\! \exists\, x,y\!: \begin{array}{r}5y\equiv1\\ \rm x+y\equiv2 \rm \end{array}\!\iff\!  \exists\, y\!:\ 5y\equiv1\!\iff gcd(5,n)=1$
