How to use systeme to write a system of equations with subscripts in the coefficients

Question

I am trying to type this system of equations:

I tried

\documentclass[12pt,a4paper]{article}
\usepackage{amsmath}
\begin{document}
    \begin{equation}
            \begin{cases}
            a_1 x+b_1 y+c_1 z=d_1, \\
            a_2 x+b_2 y+c_2 z=d_2, \\
            a_3 x+b_3 y+c_3 z=d_3.
        \end{cases}
    \end{equation}
\end{document}

With systeme package, I tried

\documentclass{article}
\usepackage{systeme}
\begin{document}
    \systeme[xyz]{
    a_1 x+b_1 y+c_1 z=d_1, 
    a_2 x+b_2 y+c_2 z=d_2, 
    a_3 x+b_3 y+c_3 z=d_3}
    \end{document}

How can I use system package to get the result?

Answer 1

You decide if it's worth the pain:

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

\begin{document}

\begin{equation}
\syssubstitute{%
  {A}{a_1}{B}{b_1}{C}{c_1}{D}{d_1}%
  {E}{a_2}{F}{b_2}{G}{c_2}{H}{d_2}%
  {I}{a_3}{J}{b_3}{K}{c_3}{L}{d_3}%
}
\systeme[xyz]{
  Ax + By + Cz = D,
  Ex + Fy + Gz = H,
  Ix + Jy + Kz = L
}
\end{equation}

\end{document}

Alternative, with comparison:

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

\begin{document}

\begin{equation}
\left\{
\renewcommand{\arraystretch}{1.2}
\setlength{\arraycolsep}{0pt}
\begin{array}{ *{3}{c >{{}}c<{{}}}c }
a_1x &+& b_1y &+& c_1z &=& d_1 \\
a_2x &+& b_2y &+& c_2z &=& d_2 \\
a_3x &+& b_3y &+& c_3z &=& d_3
\end{array}
\right.
\end{equation}

\begin{equation}
\syssubstitute{%
  {A}{a_1}{B}{b_1}{C}{c_1}{D}{d_1}%
  {E}{a_2}{F}{b_2}{G}{c_2}{H}{d_2}%
  {I}{a_3}{J}{b_3}{K}{c_3}{L}{d_3}%
}
\systeme[xyz]{
  Ax + By + Cz = D,
  Ex + Fy + Gz = H,
  Ix + Jy + Kz = L
}
\end{equation}

\end{document}