Answer
Please see the graph.
Work Step by Step
Red line: $4x-y\le0$
Blue line: $3x-2y\ge-5$
Green line: $y\ge-4$
To determine what sides of the lines to shade, we use a point not on the line. We can use (1,1) for the lines.
Red line:
$4x-y\le0$
$4*1-1\le0$
$4-1\le0$
$3\le0$ (false, so we shade the left side of the line)
Blue line:
$3x-2y\ge-5$
$3*1-2*1\ge-5$
$3-2\ge-5$
$1\ge-5$ (true, so we shade the right side of the line)
Green line:
$y\ge-4$
$1\ge-4$ (true, so we shade above the line)
The solution area is the overlap of the three inequalities. The boundary points of the solution area are $(-4.333,-4$, $(-1,-4)$, and $(1,4)$.
