1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} y = 27 \\ y = 3^x \end{cases}$$ 2. **Use substitution:** Since both expressions equal $y$, set them equal to each other: $$27 = 3^x$$ 3. **Rewrite 27 as a power of 3:** $$27 = 3^3$$ 4. **Set exponents equal:** $$3^3 = 3^x \implies x = 3$$ 5. **Find $y$:** Substitute $x=3$ into $y=3^x$: $$y = 3^3 = 27$$ 6. **Solution:** $$\boxed{(x,y) = (3, 27)}$$ This means the two equations intersect at the point where $x=3$ and $y=27$.