I'm asked to find all integers $x$ of the form $x\equiv \_5 3$, $x\equiv \_8 6$. It turns out that the set of all such integers is $$\{ x\in \mathbb{Z} : x=38+40t, \ \text{for some} \ \ t\in \mathbb{Z}\}$$
yet I haven't been able to get closer to such result. I would appreciate any help.