1. **State the problem:** Solve the linear equation $2y + 2x = -10$ for $y$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by performing algebraic operations such as addition, subtraction, multiplication, or division. 3. **Isolate $y$:** Starting with the equation: $$2y + 2x = -10$$ Subtract $2x$ from both sides: $$2y + 2x - 2x = -10 - 2x$$ which simplifies to: $$2y = -10 - 2x$$ 4. **Divide both sides by 2 to solve for $y$:** $$y = \frac{-10 - 2x}{2}$$ Use cancellation to simplify: $$y = \frac{\cancel{2}(-5 - x)}{\cancel{2}}$$ which simplifies to: $$y = -5 - x$$ 5. **Final answer:** $$y = -x - 5$$ This is the solution for $y$ in terms of $x$ from the given linear equation. Note: The second equation $y = -(x + 2)^2 - 1$ is a separate quadratic function and is not solved here as per instructions to solve only the first problem.