1. The problem is to solve a system of equations using the substitution method. 2. The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. 3. For example, if the system is: $$\begin{cases} x + y = 5 \\ 2x - y = 1 \end{cases}$$ 4. Solve the first equation for $y$: $$y = 5 - x$$ 5. Substitute $y = 5 - x$ into the second equation: $$2x - (5 - x) = 1$$ 6. Simplify the equation: $$2x - 5 + x = 1$$ $$3x - 5 = 1$$ 7. Add 5 to both sides: $$3x - \cancel{5} + \cancel{5} = 1 + 5$$ $$3x = 6$$ 8. Divide both sides by 3: $$\frac{3x}{\cancel{3}} = \frac{6}{\cancel{3}}$$ $$x = 2$$ 9. Substitute $x = 2$ back into $y = 5 - x$: $$y = 5 - 2 = 3$$ 10. The solution to the system is: $$\boxed{(x, y) = (2, 3)}$$