1. **Problem 16: Solve the system of inequalities by graphing:** Given inequalities: $$x \leq 4$$ $$y > -3x + 12$$ $$y \leq 9$$ Test the point $(0,0)$ to determine shading: - For $x \leq 4$: $0 \leq 4$ is true, so the boundary line $x=4$ is solid. - For $y > -3x + 12$: $0 > -3(0) + 12 \Rightarrow 0 > 12$ is false, so shade opposite side. - For $y \leq 9$: $0 \leq 9$ is true, so the boundary line $y=9$ is solid. The solution region is where all inequalities overlap. 2. **Problem 17: Find the cost of coffee, doughnuts, and tip from the system:** Let $C$ = cost of one coffee, $D$ = cost of one doughnut, $T$ = tip amount. From the problem: - Monday: $2C + D + T = 11.25$ - Tuesday: $C + 2D + T = 8.75$ - Wednesday: $C + 6D + T = 11.75$ Subtract Tuesday from Wednesday: $$ (C + 6D + T) - (C + 2D + T) = 11.75 - 8.75 $$ $$ 4D = 3.00 $$ $$ D = 0.75 $$ Substitute $D=0.75$ into Tuesday's equation: $$ C + 2(0.75) + T = 8.75 $$ $$ C + 1.5 + T = 8.75 $$ $$ C + T = 7.25 $$ Substitute $D=0.75$ into Monday's equation: $$ 2C + 0.75 + T = 11.25 $$ $$ 2C + T = 10.5 $$ Subtract $C + T = 7.25$ from $2C + T = 10.5$: $$ (2C + T) - (C + T) = 10.5 - 7.25 $$ $$ C = 3.25 $$ From $C + T = 7.25$: $$ 3.25 + T = 7.25 $$ $$ T = 4.00 $$ **Final costs:** - Coffee $C = 3.25$ - Doughnut $D = 0.75$ - Tip $T = 4.00$ 3. **Cost for two baker's dozens (24 doughnuts) including tip:** $$ 24D + T = 24(0.75) + 4.00 = 18 + 4 = 22.00 $$ **Summary:** - The solution region for inequalities is the overlap of $x \leq 4$, $y > -3x + 12$ (above the line), and $y \leq 9$. - Coffee costs 3.25, doughnuts 0.75 each, tip 4.00. - Two baker's dozens doughnuts with tip cost 22.00.