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. $x \leq 5$
2. $x + y \leq 7$
$x \geq 0$
$y \geq 0$
Graph $x = 5$ and $y = 7 - x$ with a solid line, but with a domain restriction of $x \geq 0, y \geq 0$
Equation 1 and 2 is $\leq$, so the shading will be to the left and below the graph, respectively.
The solution set is where the red and blue areas overlap (the answer is the purple area).
See graph below.
This solution set is bounded.
