Answer
See graph below.
Work Step by Step
The question asks to graph the solution set of the system of inequalities.
Here are some criteria for graphing inequalities:
1. If it is $\lt$ or $\gt$, then the graph must be dashed.
2. If it is $\leq$ or $ \geq$, then the graph must be solid.
3. If it is $\lt$ or $\leq$ (with y being isolated), then the shading is below, left, or inside the graph.
4. If it is $\gt$ or $\geq$ (with y being isolated), then the shading is above, right, or outside the graph.
Given:
1. $x - y \gt 0$
$-y \gt -x$
$y \lt x$
2. $4 + y \leq 2x$
$y \leq 2x - 4$
Graph $y = x$ and $y = 2x - 4$ with a dashed line and solid line, respectively.
Since both equations are either $\lt$ or $\leq$, then the shading will be below the graph.
The solution set is where the black and green areas overlap.
See graph below.
