Answer
See the graph
Work Step by Step
We graph the equations exactly like we did for the system of two inequalities.
First graph: $x + y \lt 5$ (blue)
$x +y\gt -5$ (pink)
$x-y \lt 4$ (black)
and $x - y \gt-2$ (green)
Using the shading on the attached graph, we know that the intersection of all three inequalities is the solution.