\DocumentMetadata{
testphase={
phase-III
,math,
},
pdfversion=2.0,
uncompress}
\documentclass{article}
\usepackage{amsmath}
\begin{document}
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\section{Equation groups with mutual alignment}
xxx
\begin{alignat}{2}
x& = y_1-y_2+y_3-y_5+y_8-\dots
&\quad&x\\
& = y'\circ y^* && xx\\
& = y(0) y' && xx\\
\end{alignat}
%
\end{document}