$R$ relation $R$ defined on $xRy \iff 3x+2y$ is divisible by $5$. I need to show that $R$ is an equivalence relation.

Question

I have proven that $R$ is reflexive and transitive. But I am stuck on proving that $R$ is symmetric.

I know that, we must show that it $xRy$ then $yRx$.

I did: $xRy \Rightarrow 3y + 2y = 5k$.

How do I go from here to prove $yRx$, this is where I'm suck

Answer 1

Hint: $3y+2x=(5x+5y)-(3x+2y)$.