Answer
Please see the graph.
Work Step by Step
Red line: $y\le 2x+1$
Blue line: $y\gt x+2$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Red line: $y\le 2x+1$
$y\le 2x+1$
$0\le 2*0+1$
$0 \le 0+1$
$0 \le 1$ (true)
This is true, so we shade the side of the line that has the point. The inequality has the "less than or equal to" sign, so we use a solid line.
Blue line: $y\gt x+2$
$0\gt 0+2$
$0\gt 2$ (false)
This is false, so we shade the side of the line that doesn't have the point. The inequality has the "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.
