1. **State the problem:** Solve the system of equations using substitution: $$y = x + 6$$ $$y = -2x - 3$$ 2. **Use substitution method:** Since both equations equal $y$, set them equal to each other: $$x + 6 = -2x - 3$$ 3. **Solve for $x$:** Add $2x$ to both sides: $$x + 2x + 6 = -2x + 2x - 3$$ $$3x + 6 = -3$$ Subtract 6 from both sides: $$3x + \cancel{6} - \cancel{6} = -3 - 6$$ $$3x = -9$$ Divide both sides by 3: $$\frac{3x}{\cancel{3}} = \frac{-9}{\cancel{3}}$$ $$x = -3$$ 4. **Find $y$ by substituting $x = -3$ into one of the original equations:** Using $y = x + 6$: $$y = -3 + 6 = 3$$ 5. **Solution:** The system's solution is $$\boxed{(-3, 3)}$$ This means the two lines intersect at the point $(-3, 3)$.