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

Question

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}
\begin{equation}
\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{equation}
\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}
\begin{equation}
\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{equation}
\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?

Answer 1

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

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

\begin{document}
\begin{equation}
\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{equation}
\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}
\begin{equation}
\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{equation}
\end{document}

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