Answer
$(1,13),(4.5,118)$
Work Step by Step
Given \begin{equation}
\begin{aligned}
& y=6 x^2-3 x+10 \\
& y=4 x^2+8 x+1.
\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}
6 x^2-3 x+10&=4 x^2+8 x+1 \\
6 x^2-4 x^2-3 x-8 x+10-1&=0 \\
2 x^2-11 x+9&=0.
\end{aligned}
\end{equation} Use factoring:
\begin{equation}
\begin{aligned}
2 x^2-9 x-2 x+9&=0 \\
x(2 x-9)-1(2 x-9)&=0 \\
(2 x-9)(x-1)&=0.
\end{aligned}
\end{equation} This gives \begin{equation}
\begin{array}{r}
2 x-9=0 \\
x=\frac{9}{2}=4.5 \\
x-1=0 \\
x=1.
\end{array}
\end{equation} The corresponding $y$ values are: \begin{equation}
\begin{aligned}
& y=4(4.5)^2+8(4.5)+1=118 \\
& y=4(1)^2+8(1)+1=13.
\end{aligned}
\end{equation} Solution: $$(1,13),(4.5,118).$$
