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. $x + y \leq 4$
2. $y \geq x$
Graph $y = -x + 4$ and $y = x$ with a solid line.
Since the first equation is $\leq$, then the shading will be below the graph
Since the second equation is $\geq$, then the shading will be above the graph.
The solution set is where the black and green areas overlap.
See graph below.
