1. **State the problem:** Solve the system of linear equations: $$y = 4x + 3$$ $$y = -x - 2$$ 2. **Use substitution method:** Since both expressions equal $y$, set them equal to each other: $$4x + 3 = -x - 2$$ 3. **Solve for $x$:** Add $x$ to both sides: $$4x + x + 3 = -2$$ Simplify: $$5x + 3 = -2$$ Subtract 3 from both sides: $$5x + \cancel{3} - 3 = -2 - 3$$ $$5x = -5$$ Divide both sides by 5: $$\frac{5x}{\cancel{5}} = \frac{-5}{\cancel{5}}$$ $$x = -1$$ 4. **Find $y$ by substituting $x = -1$ into one of the original equations:** Using $y = -x - 2$: $$y = -(-1) - 2$$ $$y = 1 - 2$$ $$y = -1$$ 5. **Final answer:** $$\boxed{(x, y) = (-1, -1)}$$