1. **State the problem:** We need to solve the system of inequalities graphically: $$y \leq \frac{1}{2}x - 6$$ $$y \geq x + 3$$ and find a point in the solution set. 2. **Understand the inequalities:** - The first inequality represents all points on or below the line $$y = \frac{1}{2}x - 6$$. - The second inequality represents all points on or above the line $$y = x + 3$$. 3. **Graph the boundary lines:** - For $$y = \frac{1}{2}x - 6$$, slope is $$\frac{1}{2}$$ and y-intercept is $$-6$$. - For $$y = x + 3$$, slope is $$1$$ and y-intercept is $$3$$. 4. **Find the intersection point of the two lines:** Set $$\frac{1}{2}x - 6 = x + 3$$. $$\frac{1}{2}x - 6 = x + 3$$ Subtract $$\frac{1}{2}x$$ from both sides: $$\cancel{\frac{1}{2}x} - 6 = \cancel{x} + 3 - \frac{1}{2}x$$ which simplifies to: $$-6 = \frac{1}{2}x + 3$$ Subtract 3 from both sides: $$-6 - 3 = \frac{1}{2}x + \cancel{3} - 3$$ $$-9 = \frac{1}{2}x$$ Multiply both sides by 2: $$2 \times (-9) = 2 \times \frac{1}{2}x$$ $$-18 = x$$ 5. **Find corresponding y-coordinate:** Substitute $$x = -18$$ into one of the lines, for example $$y = x + 3$$: $$y = -18 + 3 = -15$$ 6. **Solution set:** The solution set is the region where $$y \leq \frac{1}{2}x - 6$$ and $$y \geq x + 3$$ overlap. 7. **Example point in solution set:** The intersection point $$(-18, -15)$$ lies in the solution set. **Final answer:** A point in the solution set is $$\boxed{(-18, -15)}$$.