1. **State the problem:** Sarah’s Pet Store has at most 16 cats and dogs combined, and at most 9 cats. 2. **Define variables:** Let $x$ be the number of cats and $y$ be the number of dogs. 3. **Write inequalities:** - The total number of cats and dogs is at most 16: $$x + y \leq 16$$ - The number of cats is at most 9: $$x \leq 9$$ - Since the number of animals cannot be negative, also include: $$x \geq 0$$ and $$y \geq 0$$ 4. **Explain the system:** These inequalities represent the constraints on the number of cats and dogs. 5. **Graphing:** The solution region is the set of points $(x,y)$ in the first quadrant bounded by the lines $x + y = 16$ and $x = 9$, including the area below and to the left of these lines. 6. **Summary:** The system of inequalities is: $$\begin{cases} x + y \leq 16 \\ x \leq 9 \\ x \geq 0 \\ y \geq 0 \end{cases}$$ This shows all possible numbers of cats and dogs Sarah’s Pet Store can have.