Système d’équations

\documentclass{article}
\usepackage{array,mathtools}
\begin{document}
\[
\left\{
\renewcommand{\arraystretch}{1.5}
\setlength{\arraycolsep}{0pt}
\def\bvdots{\vdotswithin{=}}
\begin{array}{
 l l >{{}}c<{{}}   % a_{11} & x_1 & +
 l l >{{}}c<{{}}   % a_{12} & x_2 & +
 c >{{}}c<{{}}     % \cdots +
 l l >{{}}c<{{}} l % a_{1n} & x_n & = & b_1
}
    a_{11} & x_1 & + & a_{12} & x_2 & +       & \cdots & + & a_{1n} & x_n & =       & b_1    \\
    a_{21} & x_1 & + & a_{22} & x_2 & +       & \cdots & + & a_{2n} & x_n & =       & b_2    \\
           &     &   &        &     & \bvdots &        &   &        &     & \bvdots & \bvdots\\
    a_{m1} & x_1 & + & a_{m2} & x_2 & +       & \cdots & + & a_{mn} & x_n & =       & b_m    
\end{array}
\right.
\]
\end{document}

\documentclass{article}
\usepackage{systeme}
\begin{document}
\syssubstitute{%
  {x}{x_{1}}%
  {y}{x_{2}}%
  {z}{x_{p}}%
  {t}{\cdots}%
  {a}{a_{11}}%
  {b}{a_{12}}%
  {c}{a_{1p}}%
  {d}{k_1}%
  {e}{a_{21}}%
  {f}{a_{22}}%
  {g}{a_{2p}}%
  {h}{k_2}%
  {i}{a_{n1}}%
  {j}{a_{n2}}%
  {l}{a_{np}}%
  {m}{k_n}%
}
\systeme[xytz]{ax+by+t+cz=d,ex+fy+t+gz=h,t=t,ix+jy+t+lz=m}
\end{document}

 \documentclass{article}
\usepackage{empheq}

\begin{document}

\begin{empheq}[left=\empheqlbrace]{alignat*=3}
  a_{11} & x_1+a_{12} & & x_2+\dots+a_{1p} & & x_p=k_1 \\[1ex]
  a_{21} & x_1+a_{22} & & x_2+\dots+a_{2p} & & x_p=k_2
\end{empheq}

\end{document}