Define the relation $\mathrel{R}$ on the set of non-negative integers $\mathbb{Z} \geq 0$ by
$x\mathrel{R}y \iff 11 | 3x+8y$
Can someone please help me figure out what are the equivalence classes $x\mathrel{R}$ for $x$ in $\mathbb{Z} \geq 0$?
Note: $a|b$ means $a$ divides $b$.
$$11\,|\,3x+8y\ \overset{-11y}\iff\ 11\,|\, 3(x-y)\ \iff\ 11\,|\,x-y$$ meaning that $x$ and $y$ give the same remainder modulo $11$.