Answer
Please see the graph.
Work Step by Step
Red line: $-2x\gt y$
Blue line: $x+2y\lt 3$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Red line: $-2x\gt y$
$-2*0\gt 0$
$0 \gt 0$ (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: $x+2y\lt 3$
$0+2*0\lt3$
$0+0\lt 3$
$0 \lt 3$ (true)
This is true, so we shade the side of the line that does 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.
