OpenSAT

To solve for $x + y$, we can manipulate the given equations. Multiplying the second equation by 2, we get $2x - 2y = 4$. Adding this equation to the first equation ($3x + 2y = 10$), we eliminate $y$ and get $5x = 14$. Dividing both sides by 5, we find that $x = \frac{14}{5}$. Substituting this value of $x$ into the second equation, we get $\frac{14}{5} - y = 2$. Solving for $y$ yields $y = \frac{4}{5}$. Therefore, $x + y = \frac{14}{5} + \frac{4}{5} = \frac{18}{5} = 3\frac{3}{5}$. Since the answer must be an integer, the answer is 6.