jmc

From the first equation, we can see that $x=\frac{5}{2}y$. Substituting for $x$ in the second equation, we obtain $3\left(\frac{5}{2}y\right)-4y=7$, which reduces to $y=2$. Solving for $x$, we find that $x=5$. Therefore, $Z=(5,2)$ and our answer is $5+2=\boxed{7}$.