%%
%% The LaTeX Companion, 3ed
%%
%% Example 11-2-18 on page II-141 in "Display environments as mini-pages".
%%
%% Copyright (C) 2022 Frank Mittelbach
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%%
%% See https://www.latex-project.org/lppl.txt for details.
%%

\documentclass{tlc3examargin}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{255.0pt}

%StartShownPreambleCommands
\usepackage{amsmath}
%StopShownPreambleCommands

\begin{document}
\begin{equation}
\begin{aligned}[b]
  x^2 + y^2  &= 1               \\
  x          &= \sqrt{1-y^2}    \\
 \text{and also }y &= \sqrt{1-x^2}
\end{aligned}               \qquad
\begin{gathered}[t]
 (a + b)^2 = a^2 + 2ab + b^2    \\
 (a + b) \cdot (a - b) = a^2 - b^2
\end{gathered}
\end{equation}
\end{document}