Aligned equations inside of TikZ node.

You could use an aligned environment with inline math inside nodes, their size is automatically calculated. Here's a small example with such a node in a tree:

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[every node/.style={rectangle,draw}]
\node {Example:}
  child {node {%
  $\begin{aligned}
     a &= bx + c\\
     a+b &= d +1
  \end{aligned}$}};
\end{tikzpicture}
\end{document}

Output:

EDIT

As pointed out by Zarko in the comments, the text width option to the node already defines a minipage. Thus, the minipage environment is superfluous unless you want the minipage width different than the node width.

---

I know this is old, but, for future reference, if you want to number your equations or really want to use an align environment, you may place it inside a minipage and specify both the node text width and minipage width properties to whatever works for you.

\documentclass[border=0.5cm]{standalone}
\usepackage{tikz}
\usepackage{amsmath}

\begin{document}
\begin{tikzpicture}
    % These are needed to remove the vertical space around above and below
    % the align and flalign environments
    \setlength{\abovedisplayskip}{0pt}
    \setlength{\belowdisplayskip}{0pt}

    \node [rectangle, draw] (example) {Examples:};
    \node [rectangle, draw, right=1cm, text width=4cm] (eq1) at (example.east) {
        \begin{minipage}{\textwidth}
            \begin{align}
                x + y &= 1 \\
                x - 2y &= 1
            \end{align}
        \end{minipage}
    };
    \node [rectangle, draw, below=0.5cm, text width=4cm] (eq2) at (eq1.south) {
        \begin{minipage}{\textwidth}
            \begin{flalign}
                x + y &= 2& \\
                x - 2y &= 2&
            \end{flalign}
        \end{minipage}
    };
    \draw [->, line width=1pt] (example) -- (eq1);
    \draw [->, line width=1pt] (example) |- (eq2);
\end{tikzpicture}
\end{document}

This example also includes flalign, since I believe it looks better than align when the node has borders.