Given that $2x - 3y = 8$ and $4x + 3y = -2$, what is the product of $x$ and $y$?
To solve for $x$ and $y$, I can use the elimination method by adding the two equations together. That way, the $3y$ terms will cancel out and I will get a simpler equation involving only $x$. So, adding the two equations, I get $2x - 3y + 4x + 3y = 8 - 2$, which simplifies to $6x = 6$. Dividing both sides by $6$, I get $x = 1$. Now that I have $x$, I can plug it back into either of the original equations to find $y$. I'll choose the first one, since it has smaller coefficients. So, substituting $x = 1$ into $2x - 3y = 8$, I get $2 - 3y = 8$, which simplifies to $-3y = 6$. Dividing both sides by $-3$, I get $y = -2$. Therefore, the product of $x$ and $y$ is $x \cdot y = 1 \cdot (-2) = -2$.

