problem: In a rectangular coordinate system, the line $5y = 2x$ intersects the line $3x - 4y = 7$ at point $Z$. What is the sum of the coordinates of point $Z$?
solution: 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 $5 + 2 = \boxed{7}$.