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. $2x + 3y \gt 12$
$3y \gt 12 - 2x$
$y \gt 4 - 2/3 x$
2. $3x - y \lt 21$
$-y \lt -3x + 21$
$y \gt 3x - 21$
Graph $y = 4 - 2/3 x$ and $y = 3x - 21$ with a dashed line.
Since both equations are $\gt$, then the shading will be above the graph
The solution set is where the black and green areas overlap.
See graph below.
