Answer
The solution set is the region shaded GRAY
Work Step by Step
We will graph the solution region for each inequality.
1. (red) $x^{2}+y^{2}=4^{2}$ is a circle centered at the origin, radius = 4.
Border: solid line ( sign is $\leq )$,
Testing $(0,0):\quad 0 + 0^{2} \leq 16\quad?$
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=2 \quad $dashed line ( sign is $> )$,
x-intercept:$\quad x+0=2\quad$ point: ($2,0)$
y-intercept:$ \quad 0+y=2\quad$ point: ($0,2)$
Testing $(0,0)$:$\quad 0+0 \geq 2 \quad ?$
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