1. **Problem Statement:** Find the values of $x$ and $y$ in the parallelogram with side lengths labeled as $2x + 2$, $2y + 2$, $3x - 7$, and $3y - 11$. 2. **Key Property:** In a parallelogram, opposite sides are equal in length. 3. **Set up equations:** - Opposite sides equality gives: $$2x + 2 = 3x - 7$$ $$2y + 2 = 3y - 11$$ 4. **Solve for $x$:** $$2x + 2 = 3x - 7$$ Subtract $2x$ from both sides: $$2 = x - 7$$ Add $7$ to both sides: $$x = 9$$ 5. **Solve for $y$:** $$2y + 2 = 3y - 11$$ Subtract $2y$ from both sides: $$2 = y - 11$$ Add $11$ to both sides: $$y = 13$$ 6. **Final answer:** $$x = 9, \quad y = 13$$ This completes the solution for the first parallelogram problem.