1. **State the problem:** Solve the system of equations using the method of substitution: $$x - 2y = 3$$ $$5x + 4y = 8$$ 2. **Isolate one variable:** From the first equation, solve for $x$ in terms of $y$: $$x - 2y = 3 \implies x = 3 + 2y$$ 3. **Substitute into the second equation:** Replace $x$ in the second equation with $3 + 2y$: $$5(3 + 2y) + 4y = 8$$ 4. **Simplify and solve for $y$:** $$15 + 10y + 4y = 8$$ $$15 + 14y = 8$$ $$14y = 8 - 15$$ $$14y = -7$$ $$y = \frac{-7}{14}$$ $$y = -\frac{1}{2}$$ 5. **Substitute $y$ back to find $x$:** $$x = 3 + 2\left(-\frac{1}{2}\right)$$ $$x = 3 - 1$$ $$x = 2$$ 6. **Final answer:** $$\boxed{(x, y) = (2, -\frac{1}{2})}$$