If $x^2 + y = 4$ and $x^4 +y^2 = 10$, then what is $x^2y$?
Maybe I can eliminate $y$ by squaring the first equation and using the second equation. If I square the first equation, I get $(x^2 + y)^2 = x^4 + 2x^2y + y^2 = 16$. Now I can substitute $y^2 = 10 - x^4$ from the second equation and get $x^4 + 2x^2y + 10 - x^4 = 16$. Simplifying, I get $2x^2y = 6$. Dividing by 2, I get $x^2y = 3$.

