Answer
See the graph
![](https://gradesaver.s3.amazonaws.com/uploads/solution/5923e93c-65e9-480f-9dae-93181e5674bb/result_image/1594463445.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020846Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=1aa157228c96e52bf0659214779ad371c994466c3f8fb4da73847ea454321bff)
Work Step by Step
We are given
$2x-y \gt 0$
$ \rightarrow y \lt 2x$
$3x+2y \leq -14$
$\rightarrow 2y \leq -3x -14$
$\rightarrow y \leq -\frac{3}{2}x-7$
Graph the boundary lines $y \lt 2x$ and $y \leq -\frac{3}{2}x-7$.
For $y \lt 2x$, use a dashed boundary line and shade below it. For $y \leq -\frac{3}{2}x-7$, use a solid boundary line and shade above it.
The bold pink region of overlap contains the system’s solutions.