Numbering two sets of equations

Question

There are many question and answers already on the subject, but I have not found any suitable one for my request, so I hope you can help me.

I have two quite big systems of equations, one is the log-linearization of the other. I would like numbering of the form:

\section{First section}
... (1a)
... (2a)
... (3a)
\section{Second section}
... (1b)
... (2b)
... (3b)

where the ellipses stand for equations. As one equation exactly relates to the other, I find this a much better structure in my thesis than simply writing equations (1) to (6). Also, I am not too fixated on the exact notation, so if someone has a better way of doing this, I am eager to here it.

Here is a MWE:

\documentclass[a4paper,12pt]{report}
\usepackage{amsmath,amsfonts,amssymb} 
\usepackage{textcomp,mathrsfs,xcolor,float,fancyhdr} 
\usepackage[latin1]{inputenc} 
\usepackage[T1]{fontenc} \pagenumbering{arabic}


\begin{document}
\chapter{Equilibrium}

\section{Deflated Equilibrium}
\begin{equation}
a=b
\end{equation}
\begin{align}
b=c \\ 
c=d
\end{align}
\section{Log-Lin Equilibrium}
\begin{equation}
a=b
\end{equation}
\begin{align}
b=c \\
c=d
\end{align}

\end{document}} 

Answer 1

Providing the instructions

\numberwithin{equation}{section}
\renewcommand\theequation{\arabic{equation}\alph{section}}

should let you achieve your formatting objective. That said, you may want to think about what your readers are supposed to learn when they encounter equations numbered, say, "(1a)" in chapters 1, 2, and 3...

\documentclass[a4paper,12pt]{report}
\usepackage{amsmath} % for \numberwithin macro and 'align' env.
\numberwithin{equation}{section} % tie `equation` counter to `section` counter
\renewcommand\theequation{\arabic{equation}\alph{section}}

\begin{document}
\refstepcounter{chapter} % just for this example

\section{Deflated Equilibrium}
\begin{equation}
a=b
\end{equation}
\begin{align}
b=c \\ 
c=d
\end{align}

\section{Log-Lin Equilibrium}
\begin{equation}
a=b
\end{equation}
\begin{align}
b=c \\
c=d
\end{align}

\end{document}