1. **State the problem:** Solve the system of equations by graphing: $$y = -x^2 + 4x + 2$$ $$y = x - 2$$ Find the points where the parabola and the line intersect. 2. **Set the equations equal to find intersection points:** Since both equal $y$, set: $$-x^2 + 4x + 2 = x - 2$$ 3. **Bring all terms to one side:** $$-x^2 + 4x + 2 - x + 2 = 0$$ Simplify: $$-x^2 + 3x + 4 = 0$$ 4. **Multiply both sides by $-1$ to simplify:** $$\cancel{-}1 \times (-x^2 + 3x + 4) = \cancel{-}1 \times 0$$ $$x^2 - 3x - 4 = 0$$ 5. **Factor the quadratic:** $$x^2 - 3x - 4 = (x - 4)(x + 1) = 0$$ 6. **Solve for $x$:** $$x - 4 = 0 \Rightarrow x = 4$$ $$x + 1 = 0 \Rightarrow x = -1$$ 7. **Find corresponding $y$ values using $y = x - 2$:** For $x=4$: $$y = 4 - 2 = 2$$ For $x=-1$: $$y = -1 - 2 = -3$$ 8. **Write the solutions as ordered pairs:** $$(-1, -3) \quad \text{and} \quad (4, 2)$$ **Final answer:** The solutions to the system are $(-1, -3)$ and $(4, 2)$.