[Tex/LaTex] Aligning ‘implies’ sign but centre equations

Question

I would like the implies sign to be aligned for a group of equations, I am able to do this using the alignat environment

\begin{alignat*}{1}
   &\implies\quad x^2 + 2yx + 14y + y^2 = 5\\
   &\implies\quad r^2 + z^2 = 10\\
   &\implies\quad r=5\\
\end{alignat*}

However, this results in all the equations being left-justified. I would like them to be centred while the implied sign remains aligned. Somewhat similar to doing

\begin{gather*}
    \implies\quad x^2 + 2yx + 14y + y^2 = 5\\
    \implies\quad r^2 + z^2 = 10\\
    \implies\quad r=5\\
\end{gather*}

but with the implies sign as it was in the previously.

So, how do I align just 1 bit of a group of equations while everything else is centred?

Answer 1

As an alternative, here it is as a TABstack.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tabstackengine}[2016-10-04]
\TABstackMath
\begin{document}
\[
\setstackgap{L}{1.3\baselineskip}
\tabularCenterstack{rc}{
   \implies& x^2 + 2yx + 14y + y^2 = 5\\
   \implies& r^2 + z^2 = 10\\
   \implies& r=5
}
\]
\end{document}

More conventionally, the array environment could be used

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\renewcommand\arraystretch{1.3}
\begin{array}{rc}
   \implies& x^2 + 2yx + 14y + y^2 = 5\\
   \implies& r^2 + z^2 = 10\\
   \implies& r=5
\end{array}
\]
\end{document}