%%
%% The LaTeX Companion, 3ed
%%
%% Example 11-2-40 on page II-153 in "Subordinate numbering sequences".
%%
%% 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{135.0pt}

%StartShownPreambleCommands
\usepackage{amsmath}
%StopShownPreambleCommands

\begin{document}
\begin{subequations}  \label{eq:1}
\begin{align}  f  &= g            \label{eq:1A} \\
               f' &= g'           \label{eq:1B} \\
    \mathcal{L}f  &= \mathcal{L}g \label{eq:1C}
\end{align}
\end{subequations}
\begin{subequations}  \label{eq:2}
\renewcommand\theequation
             {\theparentequation\roman{equation}}
\begin{align}  f  &= g            \label{eq:2A} \\
               f' &= g'           \label{eq:2B} \\
    \mathcal{L}f  &= \mathcal{L}g + K  \label{eq:2C}
\end{align}
\end{subequations}
Note the relationship between~\eqref{eq:1}
and~\eqref{eq:2}: only~\ref{eq:1C} and~\ref{eq:2C} differ.
\end{document}