Solving Linear–Quadratic Systems Practice Test

A ball follows the path $y=-x^2+6x$ (a parabola). A laser beam follows the line $y=2x$. Where do they intersect? Solve the system.

$$\begin{cases} y = -x^2 + 6x \\ y = 2x \end{cases}$$

Solve the linear-quadratic system algebraically (by substitution). The solution(s) correspond to the intersection point(s) of the line and the parabola.

$$\begin{cases}

y = x + 1 \

y = x^2 - 2x + 1

\end{cases}$$

What are all solution(s) $(x,y)$?