1. **Problem statement:** Stephen starts with 16 points and only makes 2-point shots. Robert starts with 14 points and only makes 3-point shots. For every shot Stephen makes, Robert makes one too. At the end of the third quarter, they are tied. 2. **Define variables:** Let $x$ be the number of shots each player made during the third quarter. 3. **Write equations:** - Stephen's total points after the third quarter: $y_S = 16 + 2x$ - Robert's total points after the third quarter: $y_R = 14 + 3x$ 4. **Since they are tied at the end:** $$16 + 2x = 14 + 3x$$ 5. **Solve for $x$:** $$16 + 2x = 14 + 3x$$ $$16 - 14 = 3x - 2x$$ $$2 = x$$ 6. **Calculate total points for each player:** - Stephen: $$y_S = 16 + 2(2) = 16 + 4 = 20$$ - Robert: $$y_R = 14 + 3(2) = 14 + 6 = 20$$ **Final answers:** - a. System of equations: $$\begin{cases} y_S = 16 + 2x \\ y_R = 14 + 3x \end{cases}$$ - b. Number of shots made by each player: $x = 2$ - c. Points each player earned by the end of the third quarter: $20$ points each