How to add a centered systeme inside an unnumbered list (itemize)

I am trying to obtain this:

I use itemize and \systeme

\begin{itemize}
\item $\systeme*{3 - 4x > 5,6 + 9x \leq 1}$
\item $\systeme*{3x -6 > 2x,2x - 6 > 5x}$
\end{itemize}


But I end up with:

I would like that the bullet from the unordered list to be centered in the \systeme.

Thank you!

I add my answer using the enviroment cases instead of systeme package with the simple common package amsmath.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath}
\begin{document}
\begin{itemize}
\item $\mathrel{\mkern-15mu}\begin{cases} 3 - 4x > 5&\\ 6 + 9x \leq 1 \end{cases}$
\item $\mathrel{\mkern-15mu}\begin{cases} 3x -6 > 2x&\\ 2x - 6 > 5x \end{cases}$
\end{itemize}
\end{document}


If you want to approach the point (bullet) near the system symbol you can increase the value 15mu (always with the minus sign) and, from the output, you see what is your preferred distance.

• Thank you @Sebastiano – Cristi Ghinea May 23 at 19:25
• @CristiGhinea Welcome to the TeX.SE. My best regards. – Sebastiano May 23 at 19:25

You were almost there! All you need to change is to replace the display-math setting with an inline-math setting, i.e., replace the $...$ wrapper with $...$.

\documentclass{article}
\usepackage{systeme}
\begin{document}
\begin{itemize}
\item $\systeme*{3 - 4x > 5,6 + 9x \leq 1}$
\item $\systeme*{3x -6 > 2x,2x - 6 > 5x}$
\end{itemize}
\end{document}


Here are two solutions for horizontally and vertically centred systems:

\documentclass{article}
\usepackage[svgnames]{xcolor}
\usepackage{mathtools}
\usepackage{systeme}
\usepackage{showframe}
\renewcommand{\ShowFrameLinethickness}{0.2pt}

\begin{document}

\mbox{}
\begin{itemize}
\item \makebox[\linewidth]{$\systeme*{3 - 4x > 5,6 + 9x \leq 1}$}
\item \hfill $\systeme*{3x -6 > 2x,2x - 6 > 5x}$\hfill\null
\end{itemize}

\end{document}