1. **State the problem:** Solve the system of equations using the substitution method: $$\begin{cases} 5x + 4y = 37 \\ x = 2y - 1 \end{cases}$$ 2. **Substitution method formula:** Substitute the expression for $x$ from the second equation into the first equation. 3. **Substitute $x = 2y - 1$ into the first equation:** $$5(2y - 1) + 4y = 37$$ 4. **Simplify and solve for $y$:** $$10y - 5 + 4y = 37$$ $$14y - 5 = 37$$ $$14y = 37 + 5$$ $$14y = 42$$ $$y = \frac{42}{14} = 3$$ 5. **Find $x$ using $x = 2y - 1$:** $$x = 2(3) - 1 = 6 - 1 = 5$$ 6. **Solution:** The ordered pair solution is $$\boxed{(5, 3)}$$ This means the system has a unique solution where $x=5$ and $y=3$.