# Centering \vdots in a system of many equations and aligning the equations to the opening brace

I have a problem similar to this question.

I want to typeset k equations with the horizontal \dots and the \vdots aligned. The problem is that I want the equations to be aligned to the opening brace.

For example the following code:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
$$\left\lbrace % \begin{split} a + b + &\dots + c = d \\ a + b + &\dots + c = d \\ &\setbox0\hbox{=}\mathrel{\makebox[\wd0]{\vdots}} \\ aaaaaaa + b + &\dots + c = d \end{split} % \right.$$
\end{document}


Produces:

As you can see the first two equations start far from the brace. So I tried this:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
$$\left\lbrace % \begin{split} &a + b + &\dots + c = d \\ &a + b + &\dots + c = d \\ & &\setbox0\hbox{=}\mathrel{\makebox[\wd0]{\vdots}} \\ &aaaaaaa + b + &\dots + c = d \end{split} % \right.$$
\end{document}


That yields what I want, but the vertical dots are not centered under the horizontal dots:

How can I obtain the alignment as in the second image but with the vertical dots aligned as in the first example?

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In this case split is not the best choice; rather use array:

\documentclass{article}
\usepackage{amsmath,array}

\begin{document}
$$\left\lbrace \begin{array}{@{} l<{{}} @{} l @{}} a + b + &\dots + c = d \\ a + b + &\dots + c = d \\ &\sbox0{\dots}\makebox[\wd0]{\vdots} \\ aaaaaaa + b + &\dots + c = d \end{array} \right.$$
\end{document}


With the addition of <{{}} an empty object is inserted so that the spacing around the operation symbols is correct.

You can also simplify the input by adding another alignment point:

\documentclass{article}
\usepackage{amsmath,array}

\begin{document}
$$\left\lbrace \begin{array}{@{} l<{{}} @{} c @{} >{{}}l @{}} a + b + &\dotsb & + c = d \\ a + b + &\dotsb & + c = d \\ &\vdots \\ aaaaaaa + b + &\dotsb & + c = d \end{array} \right.$$
\end{document}


(Notice the use of \dotsb in this case, to get the right dots.)

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