1. **State the problem:** Solve the system of equations using the equal value method: $$y = x^2 - x - 2$$ $$y = x - 6$$ 2. **Explain the equal value method:** Since both expressions equal $y$, set them equal to each other: $$x^2 - x - 2 = x - 6$$ 3. **Solve the equation:** Move all terms to one side: $$x^2 - x - 2 - x + 6 = 0$$ Simplify: $$x^2 - 2x + 4 = 0$$ 4. **Check for factorization or use quadratic formula:** The quadratic is $$x^2 - 2x + 4 = 0$$ Calculate the discriminant: $$\Delta = (-2)^2 - 4 \times 1 \times 4 = 4 - 16 = -12$$ Since $\Delta < 0$, there are no real solutions. 5. **Interpretation:** The system has no real intersection points; the parabola and the line do not cross. **Final answer:** No real solutions for $x$; the system has no real points of intersection.