Equation sublabeling

This is a trick I learned from this nice answer by the author of the witharrows package, which has a lot of hidden gems I did not appreciate enough before.

The point is that you can use witharrows even without arrows.

\documentclass[12 pt,handout,notheorems, serif]{beamer}
%\documentclass[12 pt]{article}
\usepackage{pgfpages}
\pgfpagesuselayout{resize to}[a4paper,landscape]
\usetheme{Boadilla}
\usefonttheme{professionalfonts} %To get the accents aligned correctly, albeit in Computer Modern Roman
\usepackage{cancel}
\usepackage{amsmath}
\usepackage{mleftright}
\usepackage{witharrows}
\renewcommand{\left}{\mleft}%<- seriously?
\renewcommand{\right}{\mright}%<- seriously?
\begin{document}
    \setcounter{equation}{14}
    \begin{equation}
        F = ma
    \end{equation}
    \begin{subequations}
    \begin{DispWithArrows}< \delta\left(t\right)= >
            \infty\;,\quad & t = 0\;,\\
            0\;,\quad & t \neq 0\;.
    \end{DispWithArrows}
    \end{subequations}
    \begin{subequations}
    \begin{DispWithArrows}< u\left(t\right)= >
            1\;,\quad  & t \geq 0\;,\\
            0\;,\quad  & t < 0\;.
    \end{DispWithArrows}
    \end{subequations}
    \begin{equation}
        v = \omega r
    \end{equation}
\end{document}

Or with left aligned columns and \mleftright as suggested by Mico.

\documentclass[12 pt,handout,notheorems, serif]{beamer}
%\documentclass[12 pt]{article}
\usepackage{pgfpages}
\pgfpagesuselayout{resize to}[a4paper,landscape]
\usetheme{Boadilla}
\usefonttheme{professionalfonts} %To get the accents aligned correctly, albeit in Computer Modern Roman
\usepackage{cancel}
\usepackage{amsmath}
\usepackage{mleftright}
\usepackage{witharrows}
\mleftright
% \renewcommand{\left}{\mleft}%<- seriously?
% \renewcommand{\right}{\mright}%<- seriously?
\begin{document}
    \setcounter{equation}{14}
    \begin{equation}
        F = ma
    \end{equation}
    \begin{subequations}
    \begin{DispWithArrows}< \delta\left(t\right)= >
            \infty\;,\quad & t = 0\;,\\
            \pgfmathsetmacro{\myw}{width("$\infty$")}\makebox[\myw pt][l]{$0$}\;,\quad & t \neq 0\;.
    \end{DispWithArrows}
    \end{subequations}
    \begin{subequations}
    \begin{DispWithArrows}< u\left(t\right)= >
            1\;,\quad  & t \geq 0\;,\\
            0\;,\quad  & t < 0\;.
    \end{DispWithArrows}
    \end{subequations}
    \begin{equation}
        v = \omega r
    \end{equation}
\end{document}

With subnumcases defined in the cases package:

\documentclass[12 pt,handout,notheorems, serif]{beamer}
\usetheme{Boadilla}
\usefonttheme{professionalfonts} 

\usepackage{cases}
\usepackage{amsmath}

\begin{document}
    \setcounter{equation}{14}
\begin{frame}
    \begin{equation}
        F = ma
    \end{equation}   
\begin{subnumcases}{\delta(t) = }
\infty  & $t = 0$,    \\
     0  & $t \neq 0$.
\end{subnumcases}
\begin{subnumcases}{u(t)=}
    1   & $t \geq 0$,   \\
    0   & $t < 0$.
\end{subnumcases}
    \begin{equation}
        v = \omega r
    \end{equation}
\end{frame}
\end{document}

Just for the sake of variety, here's a solution which uses the cases package and its subnumcases environment.

\documentclass[12pt,handout,notheorems, serif]{beamer}
\usetheme{Boadilla}
\usefonttheme{professionalfonts}
\usepackage{pgfpages}
\pgfpagesuselayout{resize to}[a4paper,landscape]
\usepackage{cases} % for 'subnumcases' environment
% 'amsmath' is loaded automatically by 'beamer' class
\begin{document}
\setcounter{equation}{14}
\begin{frame}
    \begin{equation}
        F = ma
    \end{equation}
    \begin{subnumcases}{\delta(t)=}
        \infty & $t = 0$,\\
        0      & $t \neq 0$.
    \end{subnumcases}
    \begin{subnumcases}{u(t)=}
        1 & $t \geq 0$,\\
        0 & $t < 0$.
    \end{subnumcases}
    \begin{equation}
        v = \omega r
    \end{equation}
\end{frame}
\end{document}