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.

Note that
$$x + y = 2 \iff 2x - 3(2-x) = 3 \iff 5x = 9$$
This equation has a solution when...
