1. **State the problem:** Solve the system of equations: $$\begin{cases} x + y = 8 \\ x - y = -4 \end{cases}$$ 2. **Formula and rules:** To solve a system of linear equations, you can use substitution or elimination. Here, elimination is straightforward. 3. **Add the two equations:** $$ (x + y) + (x - y) = 8 + (-4) $$ Simplify: $$ 2x = 4 $$ 4. **Solve for $x$:** $$ x = \frac{4}{2} = 2 $$ 5. **Substitute $x=2$ into the first equation:** $$ 2 + y = 8 $$ 6. **Solve for $y$:** $$ y = 8 - 2 = 6 $$ 7. **Final answer:** $$ (x, y) = (2, 6) $$ This is the solution to the first system of equations.