1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + y = -3 \\ x - y = 11 \end{cases}$$ 2. **Formula and rules:** To solve a system of two linear equations, we can use the method of addition (elimination) or substitution. Here, addition is convenient because adding the two equations will eliminate $y$. 3. **Add the two equations:** $$ (x + y) + (x - y) = -3 + 11 $$ Simplify: $$ x + y + x - y = 8 $$ $$ 2x = 8 $$ 4. **Divide both sides by 2:** $$ \cancel{2}x = \cancel{2}4 $$ $$ x = 4 $$ 5. **Substitute $x=4$ into the first equation:** $$ 4 + y = -3 $$ 6. **Solve for $y$:** $$ y = -3 - 4 $$ $$ y = -7 $$ 7. **Final answer:** $$ x = 4, \quad y = -7 $$ This means the two lines intersect at the point $(4, -7)$.