Answer
Please see the graph.
Work Step by Step
Red line: $y\gt 2$
Blue line: $x\ge -1$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Red line: $y\gt 2$
$0\gt 2$ (false)
This is false, so we shade the side of the line that doesn't have the point. The inequality has the "greater than" sign, so we use a dotted line.
Blue line: $x\ge -1$
$x\ge -1$
$0 \ge -1$ (true)
This is true, so we shade the side of the line that does have the point. The inequality has the "less than or equal to" sign, so we use a solid line.
The solution area for the system on inequalities is the area that is shaded both blue and red.
