1. **State the problem:** Solve the system of equations using substitution: $$y = 4x - 9$$ $$y = x - 3$$ 2. **Formula and method:** Since both expressions equal $y$, set them equal to each other: $$4x - 9 = x - 3$$ 3. **Solve for $x$:** Subtract $x$ from both sides: $$4x - x - 9 = -3$$ Simplify: $$3x - 9 = -3$$ Add 9 to both sides: $$3x = 6$$ Divide both sides by 3: $$x = 2$$ 4. **Find $y$:** Substitute $x=2$ into one of the original equations, for example $y = x - 3$: $$y = 2 - 3 = -1$$ 5. **Solution:** The solution to the system is: $$(x, y) = (2, -1)$$ This means the two lines intersect at the point $(2, -1)$.