1. **State the problem:** We need to determine which point among (0,10), (10,8), (0,8), and (2,8) is NOT a solution to the system of inequalities: $$y > \frac{5}{2}x + 6$$ $$y \geq 3x + 1$$ 2. **Recall the rules:** - For $y > \frac{5}{2}x + 6$, the point's $y$ must be strictly greater than $\frac{5}{2}x + 6$. - For $y \geq 3x + 1$, the point's $y$ must be greater than or equal to $3x + 1$. 3. **Test each point:** - For $(0,10)$: - Check $y > \frac{5}{2}x + 6$: $10 > \frac{5}{2} \times 0 + 6 = 6$ is true. - Check $y \geq 3x + 1$: $10 \geq 3 \times 0 + 1 = 1$ is true. - So, $(0,10)$ satisfies both. - For $(10,8)$: - Check $y > \frac{5}{2}x + 6$: $8 > \frac{5}{2} \times 10 + 6 = 25 + 6 = 31$ is false. - Since the first inequality fails, $(10,8)$ is NOT a solution. - For $(0,8)$: - Check $y > \frac{5}{2}x + 6$: $8 > 6$ is true. - Check $y \geq 3x + 1$: $8 \geq 1$ is true. - So, $(0,8)$ satisfies both. - For $(2,8)$: - Check $y > \frac{5}{2}x + 6$: $8 > \frac{5}{2} \times 2 + 6 = 5 + 6 = 11$ is false. - Since the first inequality fails, $(2,8)$ is NOT a solution. 4. **Conclusion:** Points $(10,8)$ and $(2,8)$ do not satisfy the system, but since the question asks for which point would NOT be a solution, the first such point in the list is $(10,8)$. **Final answer:** $(10,8)$