How to number each equation of simultaneous equations grouped by a left curly brace?

See the empheq package.

\documentclass[a4paper]{memoir}
\usepackage{empheq} % autoloads mathtols and amsmath
\begin{document}
\begin{empheq}[left=\empheqlbrace]{align}
ax + by =c \\
px + qy = r 
\end{empheq}
\end{document}

There is the main MWE of a simple example involving multimple cases:

\documentclass[preview,border=12pt,varwidth]{standalone} 
\usepackage{amsmath}
%
\begin{document}
\abovedisplayskip=0pt\relax
\[
\left\{
\begin{array}{cc}
 ax + by =c & \refstepcounter{equation}(\theequation)\\
 ax + by =c & \refstepcounter{equation}(\theequation)
\end{array}
\right.
\]
%
\end{document}

If you want to change the spacing of the delimiter before the equations, add this lines to the preamble of the MWE:

\usepackage{etoolbox}
\AtBeginEnvironment{array}{%
 \addtolength{\arraycolsep}{-3.5pt}
 \renewcommand{\arraystretch}{1.1}%
}