1. **State the problem:** Solve the system of linear equations: $$-x + y = 4$$ $$y = 2x + 2$$ Find the values of $x$ and $y$ where these two lines intersect. 2. **Use substitution method:** Since the second equation is already solved for $y$, substitute $y = 2x + 2$ into the first equation. $$-x + (2x + 2) = 4$$ 3. **Simplify the equation:** $$-x + 2x + 2 = 4$$ $$x + 2 = 4$$ 4. **Solve for $x$:** $$x + 2 = 4$$ $$x = 4 - 2$$ $$x = 2$$ 5. **Find $y$ by substituting $x=2$ into $y = 2x + 2$:** $$y = 2(2) + 2$$ $$y = 4 + 2$$ $$y = 6$$ 6. **Final answer:** The lines intersect at the point $(2, 6)$.