How do I center the equation number in an align block with intertext?

Question

I would like to format a 2-line (or any even number) equation with a centered tag and some left-justified text within the equation. In other words, can I achieve the tag placement as in the first case below while having some left-aligned text as in the 2nd or 3rd case below? (I'm okay with either.)

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

\begin{document}

\begin{equation}
\begin{aligned}
y&=ax+b\\
z&=cy+d
\end{aligned}
\end{equation}

\hrule

\begin{align}
y&=ax+b\\
\shortintertext{and} z&=cy+d
\end{align}

\hrule

\begin{flalign}
&& y&=ax+b&\\
\text{and} && z&=cy+d&
\end{flalign}

\end{document}

Answer 1

These are two dirty hacks with flalign: a) put the intertext at the beginning of a middle line, adjust the spacing and number only this middle line; b) insert aligned inside an empheq{flalign} environment and use the `left= è optional argument for empheq.

I also propose a third solution with the text between the two lines, but not at the left margin:

 \documentclass{article}
\usepackage{empheq}
\usepackage[showframe]{geometry}

\begin{document}

\begin{flalign}
  && y&=ax+b&\notag\\[-1ex]
  \rlap{and} \\[-1ex]
  && z&=cy+d&\notag
\end{flalign}

\begin{empheq}[left =\rlap{and}\qquad]{flalign}
  \begin{aligned}
    y & =ax+b \\[2ex]
    z & =cy+d
  \end{aligned}
\end{empheq}
\smallskip

\begin{equation}\label{eq-c}
  \begin{alignedat}{2}
    && y&=ax+b\\
    \ArrowBetweenLines[\llap{and\qquad}]
    && z&=cy+d \quad
  \end{alignedat}
\end{equation}

\end{document} 

Answer 2

If you are using plain TeX then you can write something like this:

$$
  \eqalignno{
     y & =ax+b \cr
     \noalign{\hbox to\hsize{and\hfil (1)}}
     z & =cy+d \cr
  }
$$

\bye