1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + y = 6 \\ x - y = 2 \end{cases}$$ 2. **Formula and rules:** To solve a system of linear equations, we can use the addition (elimination) method or substitution method. Here, elimination is straightforward. 3. **Step-by-step solution:** - Add the two equations to eliminate $y$: $$ (x + y) + (x - y) = 6 + 2 $$ $$ 2x = 8 $$ - Solve for $x$: $$ x = \frac{8}{2} = 4 $$ - Substitute $x=4$ into the first equation: $$ 4 + y = 6 $$ - Solve for $y$: $$ y = 6 - 4 = 2 $$ 4. **Answer:** The solution to the system is $$ (x, y) = (4, 2) $$ This means the two lines intersect at the point $(4, 2)$.