1. **State the problem:** Solve the system of linear equations using substitution method. 2. **General approach:** The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. 3. **Example system:** Suppose the system is: $$\begin{cases} x + y = 5 \\ 2x - y = 1 \end{cases}$$ 4. **Step 1:** Solve the first equation for $y$: $$y = 5 - x$$ 5. **Step 2:** Substitute $y = 5 - x$ into the second equation: $$2x - (5 - x) = 1$$ 6. **Step 3:** Simplify the equation: $$2x - 5 + x = 1$$ $$3x - 5 = 1$$ 7. **Step 4:** Solve for $x$: $$3x = 1 + 5$$ $$3x = 6$$ $$x = \frac{6}{3}$$ $$x = 2$$ 8. **Step 5:** Substitute $x=2$ back into $y = 5 - x$: $$y = 5 - 2$$ $$y = 3$$ 9. **Final answer:** The solution to the system is: $$\boxed{(x, y) = (2, 3)}$$