Answer
Please see the graph.
Work Step by Step
Red line: $x-2y\ge7$
Blue line: $x+y\le-5$
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.
Red line:
$x-2y\ge7$
$0-2*0\ge7$
$0-0\ge7$
$0\ge 7$ (false, so we shade the right side of the line)
Blue line:
$x+y\le-5$
$0+0\le-5$
$0\le-5$ (false, so we shade the left side of the line)
The solution area is the overlap of the two inequalities.
