1. **State the problem:** Find the solution to the system of linear equations: $$y = -2x - 9$$ $$y = -5x - 21$$ 2. **Set the equations equal to each other:** Since both expressions equal $y$, set them equal to find $x$: $$-2x - 9 = -5x - 21$$ 3. **Solve for $x$:** Add $5x$ to both sides: $$-2x + \cancel{5x} - 9 = \cancel{-5x} + 5x - 21 \Rightarrow 3x - 9 = -21$$ Add 9 to both sides: $$3x - 9 + 9 = -21 + 9 \Rightarrow 3x = -12$$ Divide both sides by 3: $$\frac{3x}{\cancel{3}} = \frac{-12}{\cancel{3}} \Rightarrow x = -4$$ 4. **Find $y$ by substituting $x = -4$ into one of the original equations:** Using $y = -2x - 9$: $$y = -2(-4) - 9 = 8 - 9 = -1$$ 5. **Final answer:** The solution to the system is: $$\boxed{(x, y) = (-4, -1)}$$