1. **State the problem:** Solve the system of equations by the addition method: $$\begin{cases} x + y = -3 \\ x - y = 11 \end{cases}$$ 2. **Formula and rules:** The addition method involves adding or subtracting the equations to eliminate one variable. 3. **Add the two equations:** $$ (x + y) + (x - y) = -3 + 11 $$ Simplify: $$ x + y + x - y = 8 $$ $$ 2x = 8 $$ 4. **Solve for $x$:** $$ x = \frac{8}{2} $$ $$ x = 4 $$ 5. **Substitute $x=4$ into the first equation:** $$ 4 + y = -3 $$ 6. **Solve for $y$:** $$ y = -3 - 4 $$ $$ y = -7 $$ 7. **Write the solution set:** $$ \{ (4, -7) \} $$ This is the unique solution to the system.