$解:因为(2x-4)²+|y-\frac{1}{2}|=0,所以2x-4=0,y-\frac{1}{2}=0,解得x=2,y=\frac{1}{2}. $
$将x=2,y=\frac{1}{2}代入\begin{cases}{mx+4y=8,}\\{5x+16y=n,}\end{cases}得\begin{cases}{2m+2=8,}\\{10+8=n,}\end{cases}$
$解得\begin{cases}{m=3,}\\{n=18.}\end{cases}$
