Answer
Please see the graph.
Work Step by Step
Blue line: $2x+3y\le-8$
Orange line: $4x-y\ge-2$
Purple line: $y\ge-5$
To determine what sides of the lines to shade, we use a point not on the line. We can use (0,0) for the lines.
Blue line:
$2x+3y\le-8$
$2*0+3*0\le-8$
$0+0 \le -8$
$0\le-8$ (false, so we shade under the line)
Orange line:
$4x-y\ge-2$
$4*0-0\ge-2$
$0-0\ge-2$
$0\ge-2$ (true, so we shade the right side of the line)
Purple line:
$y\ge-5$
$0\ge-5$ (true, so we shade above the line)
The solution area is the overlap of the three inequalities. In this case, the area is the triangle created at the three intersection points of $(−1,-2)$, $(1.75, -5)$, and $(3.5, -5)$.
