Answer
Please see the graph.
Work Step by Step
Blue line: $2x+y\le7$
Orange line: $3x-4y\ge-6$
Purple line: $y\ge-3$
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:
$2x+y\le7$
$2*0+0\le7$
$0\le7$ (true, so we shade the left side of the line)
Orange line:
$3x-4y\ge-6$
$3*0-4*0\ge-6$
$0\ge-6$ (true, so we shade the right side of the line)
Purple line:
$y\ge-3$
$0\ge-3$ (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 $(2,3)$, $(-6, -3)$, and $(5, -3)$.
