Answer
$(0,0)$ and $(8,4)$
Work Step by Step
$\left\{\begin{array}{l}{x=2 y}\\{x=y^{2}-2y}\end{array}\right.$
Graphed with desmos.com/calculator.
Substitute $x$ into the second equation,
$\begin{aligned}2y&=y^{2}-2y\\0&=y^{2}-4y\\y(y-4)&=0\end{aligned}$
$\left[\begin{array}{ll}
y=0 & y=4\\
\text{... back -substitute} & \\
& \\
x=2(0) & x=2(4)\\
x=0 & x=8\\
& \\
(0,0) & (8,4) \\
&
\end{array}\right]$