Answer
The solution set is the region shaded GRAY
Work Step by Step
We will graph the solution region for each inequality.
1. (red) $x^{2}+y^{2}=1^{2}$
is a circle centered at the origin, radius = $1$.
Border: dashed line ( sign is $> )$,
Testing $(0,0):\quad 0^{2} + 0^{2} > 1\quad?$
No, shade the region not containing $(0,0)$
1. (blue) $x^{2}+y^{2}=4^{2}$
is a circle centered at the origin, radius = $4$.
Border:$ $dashed line ( sign is $< )$,
Testing $(0,0):\quad 0 + 0^{2} < 16\quad?$
Yes, shade the region containing $(0,0)$
The solution set is the region with BOTH shadings.
The solution set is the region shaded GRAY
