1. **State the problem:** Simplify the expression $7 + 2 + 5y + 3y$. 2. **Identify like terms:** Combine constant terms and terms with $y$ separately. 3. **Combine constants:** $7 + 2 = 9$. 4. **Combine $y$ terms:** $5y + 3y = (5 + 3)y = 8y$. 5. **Write the simplified expression:** $9 + 8y$. 6. **Final answer:** The fully simplified expression is $9 + 8y$.