1. **State the problem:** We need to graph the system of inequalities: $$y < 2x + 3$$ $$y \leq 2x$$ and determine which points among A(0,3), B(3,1), C(1,2), and D(1,3) satisfy both inequalities. 2. **Graphing the inequalities:** - The line $y = 2x + 3$ is a boundary for the first inequality. Since the inequality is strict ($<$), the line is dashed, and the region below it is shaded. - The line $y = 2x$ is a boundary for the second inequality. Since the inequality is inclusive ($\leq$), the line is solid, and the region below or on it is shaded. - The solution set is the intersection of these two shaded regions. 3. **Check each point:** - Point A(0,3): - Check $y < 2x + 3$: $3 < 2(0) + 3 \Rightarrow 3 < 3$ (False, since 3 is not less than 3) - Check $y \leq 2x$: $3 \leq 2(0) \Rightarrow 3 \leq 0$ (False) - So, A is not a solution. - Point B(3,1): - Check $y < 2x + 3$: $1 < 2(3) + 3 \Rightarrow 1 < 9$ (True) - Check $y \leq 2x$: $1 \leq 2(3) \Rightarrow 1 \leq 6$ (True) - So, B is a solution. - Point C(1,2): - Check $y < 2x + 3$: $2 < 2(1) + 3 \Rightarrow 2 < 5$ (True) - Check $y \leq 2x$: $2 \leq 2(1) \Rightarrow 2 \leq 2$ (True) - So, C is a solution. - Point D(1,3): - Check $y < 2x + 3$: $3 < 2(1) + 3 \Rightarrow 3 < 5$ (True) - Check $y \leq 2x$: $3 \leq 2(1) \Rightarrow 3 \leq 2$ (False) - So, D is not a solution. **Final answer:** Points B(3,1) and C(1,2) satisfy the system of inequalities.