1. **State the problem:** Solve the system of equations using substitution: $$y = 4x - 7$$ $$y = 2x + 9$$ 2. **Formula and method:** Since both expressions equal $y$, set them equal to each other: $$4x - 7 = 2x + 9$$ 3. **Solve for $x$:** Subtract $2x$ from both sides: $$4x - \cancel{2x} - 7 = \cancel{2x} + 9 - 2x$$ $$2x - 7 = 9$$ Add 7 to both sides: $$2x - 7 + 7 = 9 + 7$$ $$2x = 16$$ Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{16}{\cancel{2}}$$ $$x = 8$$ 4. **Find $y$:** Substitute $x=8$ into one of the original equations, for example $y = 4x - 7$: $$y = 4(8) - 7 = 32 - 7 = 25$$ 5. **Solution:** The solution to the system is: $$(x, y) = (8, 25)$$