Answer
See graph below.
The solution set is bounded.
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. $4x + 3y \leq 18$
$3y \leq 18 - 4x$
$y \leq 6 - 4/3 x$
2. $2x + y \leq 8$
$y \leq 8 - 2x$
$x \geq 0, y \geq 0$
Graph $y = 6 - 4/3 x$ and $y = 8 - 2x$ with a solid line, but with a domain restriction of $x \geq 0, y \geq 0$.
Since both equations are $\leq$, then the shading will be below the graph.
The solution set is where the black and green areas overlap.
See graph below.
This solution set is bounded.
