problem: Given that $2x - 3y = 8$ and $4x + 3y = -2$, what is the product of $x$ and $y$?
solution: Adding the two equations gives $6x = 6$, so $x=1$.  Substituting this into the first equation gives $2 - 3y = 8$.  Solving for $y$ gives $y=-2$, so $xy = \boxed{-2}$.