1. **State the problem:** We have a parallelogram with sides labeled as follows: - Top side: $3y + 8$ - Left side: $5y$ - Right side: $x + 8$ - Bottom side: $2x - 4$ We need to find the values of $x$ and $y$. 2. **Recall properties of a parallelogram:** Opposite sides of a parallelogram are equal in length. 3. **Set up equations using the property:** - Top side equals bottom side: $$3y + 8 = 2x - 4$$ - Left side equals right side: $$5y = x + 8$$ 4. **Solve the system of equations:** From the second equation: $$x = 5y - 8$$ Substitute $x$ into the first equation: $$3y + 8 = 2(5y - 8) - 4$$ 5. **Simplify the equation:** $$3y + 8 = 10y - 16 - 4$$ $$3y + 8 = 10y - 20$$ 6. **Bring all terms to one side:** $$3y + 8 - 10y + 20 = 0$$ $$-7y + 28 = 0$$ 7. **Solve for $y$:** $$-7y = -28$$ $$y = \frac{\cancel{-28}}{\cancel{-7}} = 4$$ 8. **Find $x$ using $y=4$:** $$x = 5(4) - 8 = 20 - 8 = 12$$ **Final answer:** $$x = 12, \quad y = 4$$