1. **State the problem:** Solve the system of equations and understand their graph shapes: $$x - y + 2 = 0$$ $$y^2 - 8x = 0$$ 2. **Rewrite the first equation:** Express $x$ in terms of $y$: $$x = y - 2$$ 3. **Substitute into the second equation:** Replace $x$ in $y^2 - 8x = 0$: $$y^2 - 8(y - 2) = 0$$ 4. **Simplify the equation:** $$y^2 - 8y + 16 = 0$$ 5. **Recognize the quadratic:** This is a perfect square: $$ (y - 4)^2 = 0$$ 6. **Solve for $y$:** $$y - 4 = 0 \implies y = 4$$ 7. **Find $x$ using $x = y - 2$:** $$x = 4 - 2 = 2$$ 8. **Interpretation:** The system has one solution at the point $(2,4)$ where the line and parabola intersect. 9. **Graph shapes:** - The line $x - y + 2 = 0$ can be rewritten as $y = x + 2$, a straight line with slope 1. - The parabola $y^2 = 8x$ opens to the right with vertex at the origin. **Final answer:** The system intersects at the single point $$\boxed{(2,4)}$$.