1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} x - y = 4 \\ x + y = 2 \end{cases}$$ 2. **Explain the elimination method:** The goal is to eliminate one variable by adding or subtracting the equations. 3. **Add the two equations:** $$ (x - y) + (x + y) = 4 + 2 $$ Simplify: $$ x - y + x + y = 6 $$ $$ 2x = 6 $$ 4. **Solve for $x$:** $$ x = \frac{6}{2} = 3 $$ 5. **Substitute $x=3$ into one of the original equations, for example $x + y = 2$:** $$ 3 + y = 2 $$ 6. **Solve for $y$:** $$ y = 2 - 3 = -1 $$ 7. **Final solution:** $$ (x, y) = (3, -1) $$ This means the two lines intersect at the point $(3, -1)$.