1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} x + y = 5 \\ -x + 7y = 19 \end{cases}$$ 2. **Isolate one variable:** From the first equation, solve for $x$: $$x = 5 - y$$ 3. **Substitute into the second equation:** Replace $x$ in the second equation with $5 - y$: $$-(5 - y) + 7y = 19$$ 4. **Simplify and solve for $y$:** $$-5 + y + 7y = 19$$ $$8y - 5 = 19$$ $$8y = 19 + 5$$ $$8y = 24$$ $$y = \frac{24}{8}$$ $$y = 3$$ 5. **Substitute $y=3$ back to find $x$:** $$x = 5 - 3 = 2$$ 6. **Final answer:** $$\boxed{(x, y) = (2, 3)}$$ This means the solution to the system is $x=2$ and $y=3$.