Next, graph the other inequality. Here, y≤-x2+8x−12 has the boundary y=-x2+8x−12. The region corresponding to the solution set also lies inside the parabola.
The solutions to the system are solutions to both individual inequalities. Meaning, these lie in the overlapping shaded regions. Here, that is the purple area.
Since the curves in their entirety are not part of the solution set, trim them down to only border the purple region. Now, the solution set of the system is shown.