1. **State the problem:** Solve the system of equations: $$x + y = 11$$ $$x - y = 3$$ 2. **Formula and rules:** To solve a system of linear equations, we can add or subtract the equations to eliminate one variable. 3. **Add the two equations:** $$\begin{aligned} (x + y) + (x - y) &= 11 + 3 \\ x + y + x - y &= 14 \\ 2x &= 14 \end{aligned}$$ 4. **Simplify and solve for $x$:** $$x = \frac{14}{2}$$ $$x = 7$$ 5. **Substitute $x=7$ into the first equation to find $y$:** $$7 + y = 11$$ $$y = 11 - 7$$ $$y = 4$$ 6. **Final answer:** $$x = 7$$ $$y = 4$$