How can I add delimiters around the amsmath align environment?

Question

I have a group of equations and I'd like to show under some transformation, the system looks like something else. So I'd like to group the AMS Align environment inside a pair of brackets such that the align environment is vertically centered on the line and I can do something like:

(That uses the matrix environment, so the alignment is centered.)

I am using LyX.

Answer 1

\begin{equation}
  \left\{
    \begin{matrix}
      x = &  y \\
      y = & -x-\mu(x^4-1)y
    \end{matrix}
  \right\} 
  \Rightarrow  
  \left\{ 
    \begin{matrix}
      w = & -x \\
      x = & w-\mu F(x)
    \end{matrix}
\right\}
\end{equation}

Produces something closely to the thing shown above.