1. **State the problem:** Valeria spent a total of 21 on 8 games and rides. Each game costs 1.50 and each ride costs 3. We want to find the number of games $x$ and rides $y$. 2. **Set up the system of equations:** - Total number of games and rides: $$x + y = 8$$ - Total cost: $$1.5x + 3y = 21$$ 3. **Express one variable in terms of the other:** From the first equation, $$y = 8 - x$$. 4. **Substitute into the cost equation:** $$1.5x + 3(8 - x) = 21$$ 5. **Simplify and solve for $x$:** $$1.5x + 24 - 3x = 21$$ $$-1.5x + 24 = 21$$ $$-1.5x = 21 - 24$$ $$-1.5x = -3$$ $$x = \frac{-3}{-1.5} = 2$$ 6. **Find $y$ using $y = 8 - x$:** $$y = 8 - 2 = 6$$ 7. **Interpretation:** Valeria played 2 games and went on 6 rides. 8. **Graphical representation:** The system can be graphed with lines: $$y = 8 - x$$ and $$y = \frac{21 - 1.5x}{3} = 7 - 0.5x$$ The intersection point $(2,6)$ is the solution. **Final answer:** Valeria played **2 games** and went on **6 rides**.