Answer
$(-2,11), (6,-21)$
Work Step by Step
Given \begin{equation}
\begin{aligned}
& y=-4 x+3 \\
& y=x^2-8 x-9.
\end{aligned}
\end{equation} Set the two equations equal and find the values of $x$. Use the values of $x$ to find the corresponding values of $y$ and write the solutions as points, $(x,y)$.
\begin{equation}
\begin{aligned}
x^2-8 x-9&=-4 x+3 \\
x^2-8 x+4 x-9-3&=0 \\
x^2-4 x-12&=0.
\end{aligned}
\end{equation} Use the quadratic formula. \begin{equation}
\begin{aligned}
x & =\frac{-(-4) \pm \sqrt{(-4)^2-4(1)(-12)}}{2(1)}\\
& =\frac{4 \pm \sqrt{64}}{2} \\
x & = \frac{4 \pm 8}{2}\\
x & =2-4=-2 \\
x & =2+4=6.
\end{aligned}
\end{equation} The corresponding $y$ values are: \begin{equation}
\begin{aligned}
& y=-4(-2)+3=11 \\
& y=-4(6)+3=-21.
\end{aligned}
\end{equation} Solution: $$(-2,11) \quad(6,-21).$$
