Answer
Please see the graph.
Work Step by Step
Green line: $4x+3y\ge12$
Orange line: $x^2+y^2<16$
$4x+3y \ge 12$
We pick the point $(0,0)$ to determine what side of the line to shade.
$4x+3y \ge 12$
$4*0+3*0 \ge 12$
$0+0 \ge 12$
$0 \ge 12$ (false, so we don't shade the side of the line)
$x^2+y^2 <16$
This is the formula for a circle with radius 4. If the point is in the circle, it is part of the solution (since we are working with a less than sign).
The point $(3,2)$ is part of the solution, so it is in the circle.
$x^2+y^2 <16$
$3^2+2^2 <16$
$9 +4 < 16$
$13 < 16$
The overlap of the two equations is the solution to the system.
