Answer
Please see the graph.
Work Step by Step
Red line: $y\lt -2x-2$
Blue line: $y\gt x+4$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Red line: $y\lt -2x-2$
$y\lt -2x-2$
$0\lt -2*0-2$
$0 \lt 0-2$
$0 \lt -2$ (false)
This is false, so we shade the side of the line that doesn't have the point. The inequality has the "less than" sign, so we use a dotted line.
Blue line: $y\gt x+4$
$0\gt 0+4$
$0\gt 4$ (false)
This is false, so we shade the side of the line that doesn't have the point. The inequality has the "less than" sign, so we use a dotted line.
The solution area for the system on inequalities is the area that is shaded both blue and red.
