1. The problem is to find a point \((x,y)\) that satisfies both inequalities: $$y > 2x - 8$$ $$y \geq \frac{3}{2}x - 2$$ 2. We need to pick a point and check if it lies in the overlapping shaded region where both inequalities are true. 3. Test point \((6,7)\) as an example: For the first inequality: $$7 > 2(6) - 8$$ $$7 > 12 - 8$$ $$7 > 4\quad \text{(True)}$$ For the second inequality: $$7 \geq \frac{3}{2}(6) - 2$$ $$7 \geq 9 - 2$$ $$7 \geq 7\quad \text{(True)}$$ 4. Since \((6,7)\) satisfies both inequalities, it is a solution to the system. Final answer: The point \( (6, 7) \) is a solution to the system of inequalities.