Answer
$(-3,-24),(4,11)$
Work Step by Step
Given \begin{equation}
\begin{aligned}
& y=5 x-9 \\
& y=-2 x^2+7 x+15.
\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}
-2 x^2+7 x+15&=5 x-9 \\
-2 x^2+7 x-5 x+15+9&=0 \\
\frac{-2 x^2+2 x+24}{(-2)}&=\frac{0}{(-2)} \\
x^2-x-12&=0.
\end{aligned}
\end{equation} Use the quadratic formula.
\begin{equation}
\begin{aligned}
x & =\frac{-(-1) \pm \sqrt{(-1)^2-4 \cdot(1) \cdot(-12)}}{2 \cdot(1)} \\
& =\frac{1 \pm \sqrt{49}}{2} \\
x & = \frac{1\pm 7}{2} \\
x_1 &= \frac{1-7}{2}=-3 \\
x_2 &= \frac{1+7}{2}=4.
\end{aligned}
\end{equation} The corresponding $y$ values are:
\begin{equation}
\begin{aligned}
& y=5(-3)-9=-24 \\
& y=5(4)-9=11.
\end{aligned}
\end{equation} Solution: $$(-3,-24),(4,11).$$
