AMC 12 2017b Problem 3

Supposed that $x$ and $y$ are nonzero real numbers such that $\frac{3x+y}{x-3y}=-2$. What is the value of $\frac{x+3y}{3x-y}$?

\textbf{(A)}\ -3 \textbf{(B)}\ -1 \textbf{(C)}\ 1 \textbf{(D)}\ 2 \textbf{(E)}\ 3