En voici une autre :
\documentclass[10pt]{article}
% \usepackage[utf8]{inputenc}
% \usepackage[T1]{fontenc}
% \usepackage{lmodern}
\usepackage[french]{babel}
\usepackage[a4paper,left=20mm,right=20mm,top=15mm,bottom=15mm]{geometry}
\usepackage{amssymb}
\usepackage{amsmath}
\DecimalMathComma % pour les virgules dans les nombres
\begin{document}
\begin{tabular}{ccccc}
\begin{minipage}[t]{0.20\linewidth}
$\left\{
\begin{array}{lll}
\alpha_{1}-\alpha_{2}-\alpha_{3}=0\\
\alpha_{1}-\alpha_{3}=0\\
\alpha_{1}+\alpha_{2}=0\\
\end{array}
\right.$
\end{minipage}
&
\begin{minipage}[t]{0.10\linewidth}
$\implies$
\end{minipage}
&
\begin{minipage}[t]{0.20\linewidth}
$\left\{
\begin{array}{ll}
\alpha_{1}-\alpha_{2}-\alpha_{3}=0\\
\alpha_{1}=-\alpha_{2}\\
\alpha_{1}=\alpha_{3}\\
\end{array}
\right.$
\end{minipage}
&
\begin{minipage}[t]{0.10\linewidth}
$\implies$
\end{minipage}
&
\begin{minipage}[t]{0.20\linewidth}
$\left\{
\begin{array}{ll}
\alpha_{1}=0\\
\alpha_{2}=0\\
\alpha_{3}=0\\
\end{array}
\right.$
\end{minipage}
\end{tabular}
\end{document}
