1. The problem involves two inequalities: $$y \geq 3x + 1$$ and $$y \leq 3x - 3$$. 2. We want to find the solution set that satisfies both inequalities simultaneously. 3. Both lines have the same slope, 3, but different y-intercepts: 1 and -3. 4. Since the slopes are equal, the lines are parallel and will never intersect. 5. The first inequality requires $$y$$ to be greater than or equal to $$3x + 1$$, so the solution is the region above or on the line $$y = 3x + 1$$. 6. The second inequality requires $$y$$ to be less than or equal to $$3x - 3$$, so the solution is the region below or on the line $$y = 3x - 3$$. 7. Because $$3x + 1 > 3x - 3$$ for all $$x$$, the region $$y \geq 3x + 1$$ lies entirely above the region $$y \leq 3x - 3$$. 8. Therefore, there is no overlap between the two shaded regions, meaning no $$x,y$$ values satisfy both inequalities simultaneously. 9. Hence, the solution set is empty. Final answer: There are no solutions that satisfy both inequalities simultaneously.