Answer
Solutions: $(0, 0)$ and $(-1, 1)$
Work Step by Step
$$x^3 + y = 0$$ $$x^2 - y = 0$$ By using the addition method, we get the following equation: $$x^3 + x^2 + 0y = 0$$ $$x^3 + x^2 = 0$$ $$x^2(x + 1) = 0$$ where the possible solutions are $x = 0$ and $x = -1$. Choosing one of the original equations, we can "plug" these two values and solve for each respective $y$: $$x^2 - y = 0$$ $$x^2 = y$$ $$0^2 = 0 = y$$ $$OR$$ $$(-1)^2 = 1 = y$$
