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. $3x + 5y \leq 15$
$5y \leq 15 - 3x$
$y \leq 3 - 3/5 x$
2. $3x + 2y \leq 9$
$2y \leq 9 - 3x$
$y \leq 4.5 - 3/2x$
$x \geq 0, y \geq 0$
Graph $y = 3 - 3/5 x$ and $y = 4.5 - 3/2x$ 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.
