Answer
The solution set is the region shaded GRAY
.
Work Step by Step
We will graph the solution region for each inequality.
1. (red) $x^{2}+y^{2}=2^{2}$
is a circle centered at the origin, radius = $2$.
Border: solid line ( sign is $\leq )$,
Testing $(0,0):\quad 0 + 0^{2} \leq 4\quad?$
Yes, shade the region containing $(0,0)$
2 (blue) To graph a line, we need two points...unless we know it is vertical or horizontal.
$x+y=1 \quad $dashed line ( sign is $> )$,
x-intercept:$\quad x+0=1\quad$ point: ($1,0)$
y-intercept:$ \quad 0+y=1\quad$ point: ($0,1)$
Testing $(0,0)$:$\quad 0+0 > 1 \quad ?$
No, shade the region not containing (0,0)
The solution set is the region with BOTH shadings.
The solution set is the region shaded GRAY