Adding a number in front of a vertical line in bracket equations

Question

I want to add a number in front of this vertical line in this equation here but without it aligning to the middle of the equation, instead aligining to one of the equations.

\begin{equation*}
 \left. \begin{cases}
    A + B = 1 \\
    Ae + Be^2 = 2e^2 
  \end{cases} \right|
\end{equation*} 

Answer 1

(I edited this answer after the OP clarified that the number should actually come after, not before, the vertical line.)

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation*}
\left\{
 \begin{matrix*}[l]
    A + B = 1 \\
    Ae + Be^2 = 2e^2 
 \end{matrix*}  
\right|
 \begin{matrix} 
    5 \\ 
    \phantom{.}
 \end{matrix}
\qquad\qquad
\left\{
 \begin{matrix*}[l]
    A + B = 1 \\
    Ae + Be^2 = 2e^2 
 \end{matrix*}  
\right|
 \begin{matrix}
   \\ 
   9 
 \end{matrix}
\end{equation*}

\end{document}

Answer 2

\documentclass{article}
\usepackage{amsmath}
\usepackage{tabularray}
\begin{document}
\begin{equation*}
\left\{
\begin{tblr}{columns={colsep=2pt}}
A + B = 1        \\
Ae + Be^2 = 2e^2 \\
\end{tblr}
\middle|
\begin{tblr}{columns={colsep=2pt}}
5 \\
  \\
\end{tblr}
\right.
\end{equation*}

\begin{equation*}
\left\{
\begin{tblr}{columns={colsep=2pt}}
A + B = 1        \\
Ae + Be^2 = 2e^2 \\
\end{tblr}
\middle|
\begin{tblr}{columns={colsep=2pt}}
  \\
9 \\
\end{tblr}
\right.
\end{equation*}
\end{document}

Answer 3

You can use nicematrix

\documentclass{article}
\usepackage{amsmath}
\usepackage{nicematrix}

\begin{document}

\[
\begin{NiceArray}{l@{\;\;}l}
A+B=1 & e \\
Ae+Be^2=2e^2
\CodeAfter
  \SubMatrix\{{1-1}{2-1}|
\end{NiceArray}
\qquad
\begin{NiceArray}{l@{\;\;}l}
Ae+Be=e \\
Ae+Be^2=2e^2 & -1
\CodeAfter
  \SubMatrix\{{1-1}{2-1}|
\end{NiceArray}
\]

\end{document}

Answer 4

Another solution with nicematrix.

\documentclass{article}
\usepackage{nicematrix}

\begin{document}

\[
\setlength{\arraycolsep}{2pt}
\begin{NiceArray}{\{l|l}
A+B=1 & 5 \\
Ae+Be^2=2e^2
\end{NiceArray}
\qquad
\begin{NiceArray}{\{l|l}
Ae+Be=e \\
Ae+Be^2=2e^2 & 9
\end{NiceArray}
\]

\end{document}

Answer 5

Using spalign package....

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,spalign}

\begin{document}
\[
\spalignsys{A + B = 1; Ae + Be^2 = 2e^2}\left|  \begin{aligned}
    & \alpha  \\
    &    
\end{aligned}\right.\to 
\spalignsys{A + B = 1; Ae + Be^2 = 2e^2}\left|  \begin{aligned}
    &  \\
    & \beta   
\end{aligned}\right.
\]
\end{document}

or this.......

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,spalign}

\begin{document}
\[
\spalignsys{A + B = 1; eA + e^2B = 2e^2}\left|  \begin{aligned}
    & \pi  \\
    &    
\end{aligned}\right.\to 
\spalignsys{A + B = 1; eA + e^2B = 2e^2}\left|  \begin{aligned}
    &  \\
    & \lambda   
\end{aligned}\right.
\]
\end{document}