Prove that $xRy \iff 5 |(x+4y)$ is an equivalence relation.
Reflexive: $xRx$, since $x+4x = 5x$, which is a multiple of $5$.
Transitive: Suppose $xRy$ and $yRz$. Then $$x+4y=5k_1,\quad y+4z = 5k_2.$$ After adding the two and some algebraic manipulation we obtain $$x+4z = 5(k_1+k_2-y)$$ thus $xRz$.
Symmetric: Suppose $xRy$. I need to show that $yRx$. I am having trouble showing this, however. Can anyone please help me?