1. **State the problem:** Solve the system of linear equations using substitution: $$\begin{cases} 2x + y = 5 \\ x - 3y = 13 \end{cases}$$ 2. **Isolate one variable:** From the first equation, solve for $y$: $$y = 5 - 2x$$ 3. **Substitute into the second equation:** Replace $y$ in the second equation with $5 - 2x$: $$x - 3(5 - 2x) = 13$$ 4. **Simplify and solve for $x$:** $$x - 15 + 6x = 13$$ $$7x - 15 = 13$$ $$7x = 13 + 15$$ $$7x = 28$$ $$x = \frac{28}{7}$$ $$x = 4$$ 5. **Substitute $x=4$ back to find $y$:** $$y = 5 - 2(4)$$ $$y = 5 - 8$$ $$y = -3$$ 6. **Check the solution:** Substitute $x=4$ and $y=-3$ into both original equations: First equation: $2(4) + (-3) = 8 - 3 = 5$ ✓ Second equation: $4 - 3(-3) = 4 + 9 = 13$ ✓ **Final answer:** $$\boxed{(x, y) = (4, -3)}$$