Answer
Please see the graph.
Work Step by Step
The red graph is $x^{2}+y^{2}\ge9$, and the blue graph is $x^{2}+y^{2}\ge16$.
$x^{2}+y^{2}\ge9$
Since we have a greater than or equal to sign, we use a solid line. We also pick the point $(0,2)$ to determine what side of the line to shade.
$x^{2}+y^{2}\ge16$
Since we have a greater than or equal to sign, we use a solid line. We also pick the point $(0,2)$ to determine what side of the line to shade.
$(0,2)$
$x^{2}+y^{2}\ge9$
$0^2+2^2 \ge 9$
$0+4 \ge 9$
$4 \ge 9$ (false, so we shade the side of the graph without the point)
$(0,2)$
$x^{2}+y^{2}\ge16$
$0^2+2^2 \ge 16$
$0+4 \ge 16$
$4 \ge 16$ (false, so we shade the side of the graph without the point)
The overlap of the two graphs is the solution set.
