How to produce aligned math with an extra symbol on the left.

\documentclass{article}

\usepackage{amsmath}
\def\LRA{\Leftrightarrow\mkern40mu}
\pagestyle{empty}

\begin{document}

\begin{alignat}{2}
\LRA &&     A + B &= C + D \\
\LRA && C + D + F &= Y + K \\
\LRA &&         E &= F     \\
     &&         X &= Z
\end{alignat}

\end{document} 

Here's one with eplain:

\input eplain
\leftdisplays % instead of displays being centered, align them at left
$$ \leqalignno{% sets the last column on the left (despite given at right)
  2x^2+bx+c&=0\cr
  x^2+{b\over x}x&=-{c\over2}&\Leftrightarrow\cr
  x^2+{b\over x}x+{b^2\over4x^2}&={b^2-4xc}&\Leftrightarrow\cr
  \Bigl(x+{b\over 2x}\Bigr)^2&={b^2-4xc\over4x^2}&\Leftrightarrow\cr
  x+{b\over 2x}&={\pm\sqrt{b^2-4xc}\over2x}&\Leftrightarrow\cr
} $$
\bye