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I have a set of subequations that I've arranged into two columns using alignat, but currently the subequations are centered on the page. Is there a way of centering the first column of equations, so that the second column is shifted to the right?

\documentclass{article}
\usepackage{amsmath, amssymb}
\usepackage{mathtools}
\begin{subequations}
\begin{alignat}{2}
\bigcup\nolimits_{i=1}^{k} S_i &= \mathcal{I}, & \label{eqn:allpacked}\\[3pt]
S_i \cap S_j &= \emptyset &\quad &\forall \hspace{1mm} i, j \in \{1, 2,\dotsc,k\}, \hspace{1mm} i \neq j, \label{eqn:nointersect}\\[3pt]
S_i &\in \mathcal{F} & &\forall \hspace{1mm} i \in \{1,2,\dotsc,k\}.\label{eqn:feasible}
\end{alignat}
\end{subequations}

enter image description here

As you can see, the subequations are centered on the page, but I'd like to find a way of centering the first column which are the main equations.

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I have used the ambient gather (Into your code there are missed \begin{document} and \end{document}). I hope to have understood your question. The look seems better to me than the previous one. Please let me know what you think.

mathtools is a larger package of amsmath than I've deleted. enter image description here

\documentclass{article}
\usepackage{amssymb}
\usepackage{mathtools}
\begin{document}
\begin{subequations}
\begin{gather}
\bigcup\nolimits_{i=1}^{k} S_i = \mathcal{I}, \label{eqn:allpacked}\\[3pt]
\mkern 100mu S_i \cap S_j = \emptyset, \quad \forall i, j \in \{1, 2,\dotsc,k\}, \, i \neq j, \label{eqn:nointersect}\\[3pt]
S_i \in \mathcal{F}, \quad \forall \,i \in \{1,2,\dotsc,k\}.\label{eqn:feasible}
\end{gather}
\end{subequations}
\end{document}
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