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. $x + y \gt 12$
2. $y \lt 0.5x - 6$
3. $3x + y \lt 6$
Graph $y = 12 - x$, $y = 0.5x - 6$, and $y = 6 - 3x$ with a dashed line.
Equation 1 is $\gt$, so the shading will be above the graph.
Equation 2 and 3 is $\lt$, so the shading will be below the graph, respectively
BUT there is no solution! No area has an overlap of all three graphs.
See graph below.
