Answer
Solutions: $(0, 0)$ and $(-2, 8)$
Work Step by Step
$$x^3 + y = 0$$ $$2x^2 - y = 0$$ To solve this system, we can use the addition method, which results in the following: $$x^3 + 2x^2 + 0y = 0$$ $$x^3 + 2x^2 = 0$$ $$x^2(x + 2) = 0$$ $$x = 0$$ $$OR$$ $$x = -2$$ We can now substitute these values in one of the original equations to solve for their respective $y$: $$2x^2 - y = 0$$ $$2x^2 = y$$ $$2(0)^2 = 0 = y$$ $$AND$$ $$2(-2)^2 = 8 = y$$
