1. **State the problem:** Solve the system of linear equations: $$y = x + 8$$ $$x + y = 2$$ 2. **Use substitution method:** Since the first equation gives $y$ in terms of $x$, substitute $y = x + 8$ into the second equation. 3. **Substitute and simplify:** $$x + (x + 8) = 2$$ $$2x + 8 = 2$$ 4. **Isolate $x$:** $$2x = 2 - 8$$ $$2x = -6$$ 5. **Divide both sides by 2:** $$\cancel{2}x = \cancel{2} \times -3$$ $$x = -3$$ 6. **Find $y$ using $y = x + 8$:** $$y = -3 + 8 = 5$$ 7. **Final solution:** $$x = -3, \quad y = 5$$ This means the two lines intersect at the point $(-3, 5)$.