1. **State the problem:** Solve the system of equations using substitution: $$7x - 4y = 27$$ $$x = y$$ 2. **Substitution method:** Since $x = y$, substitute $y$ for $x$ in the first equation: $$7y - 4y = 27$$ 3. **Simplify the equation:** $$3y = 27$$ 4. **Solve for $y$:** $$y = \frac{27}{3}$$ $$y = 9$$ 5. **Find $x$ using $x = y$:** $$x = 9$$ 6. **Final answer:** $$x = 9, \quad y = 9$$ This means the solution to the system is the point $(9,9)$ where both equations intersect.