\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}

\begin{document}

\begin{alignat*}{3}
  a& = b &\quad & \text{if} & \quad & x\ne y\\
  c& = d &      & \text{if} &       & x = y
\end{alignat*}    


\begin{equation}\label{eq:elas:C}
\end{equation}

\begin{equation}\label{eq:elas:lam-mu}
  \lambda = \frac{E \nu}{ (1+\nu)(1-2\nu)} \qquad
\end{equation}


\begin{align}
  a & = b + c \\
  c & =
      \begin{multlined}[t]
        d + e + f + g + h + i + j \\
        + k + l + m + n + o + p + q
      \end{multlined}
\end{align}


Deleted eqnarray:
\begin{eqnarray}
a &=& 1 + 2, \label{eq:a}\\
b &=& 3 + 4, \label{eq:b}
\end{eqnarray}
Some additional text:
\begin{eqnarray}
c &=& 1 + 2, \label{eq:c}\\
d &=& 3 + 4, \label{eq:d}
\end{eqnarray}

\end{document}

