Answer
$x=\frac{1}{2} \quad$ and $\quad y=\frac{1}{\frac{1}{2}}=2$ or
$x=-\frac{1}{2} \quad$ and $\quad y=\frac{1}{-\frac{1}{2}}=-2$
Work Step by Step
We set the equations $y=1 / x$ and $y=4 x$ equal to one another.
$$
\begin{aligned}
\frac{1}{x} & =4 x \\
4 x^2 & =1 \\
x^2 & =\frac{1}{4}
\end{aligned}
$$
This gives $x=\frac{1}{2} \quad$ and $\quad y=\frac{1}{\frac{1}{2}}=2$ or
$x=-\frac{1}{2} \quad$ and $\quad y=\frac{1}{-\frac{1}{2}}=-2$
