For non-zero numbers $x,\;y$ and $z$, $3x=4y$ and $4y=3z$. What is $\large\frac{z}{x}?$

Question

$\begin{array}{1 1} (a)\; 1 \\ (b)\; \large\frac{1}{2} \\ (c)\; 2 \\ (d)\; \text{cannot be determined} \end{array}$