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