If you don't want those pesky curly braces, load the package with the straightbraces option:
\documentclass[b5paper,11pt]{article}
\usepackage{amsmath}
\usepackage[lite,straightbraces]{mtpro2} % lite because I only have that
\usepackage{systeme}
\begin{document}
\[
\systeme{2x+3y=5,x-4y=-3}
\quad
\systeme[xzy]{2x+3y-z=5,x+2z-4y=-3,x+y=2}
\]
\end{document}
Note that \sysdelim\{. is the default.
If you prefer the pesky braces, you have to use \LEFTRIGHT, so an indirect path must be followed:
\documentclass[b5paper,11pt]{article}
\usepackage{amsmath}
\usepackage[lite]{mtpro2} % lite because I only have that
\usepackage{systeme,xparse}
\NewDocumentCommand{\csysteme}{som}{%
\LEFTRIGHT\{.{%
\sysdelim..
\IfBooleanTF{#1}
{\IfNoValueTF{#2}{\systeme*{#3}}{\systeme*[#2]{#3}}}
{\IfNoValueTF{#2}{\systeme{#3}}{\systeme[#2]{#3}}}%
}%
}
\begin{document}
\[
\csysteme{2x+3y=5,x-4y=-3}
\quad
\csysteme[xzy]{2x+3y-z=5,x+2z-4y=-3,x+y=2}
\]
\end{document}
With a patch one can avoid changing syntax; the idea is to use \LEFTRIGHT of mtpro2 instead of \left and \right.
\documentclass[b5paper,11pt]{article}
\usepackage{amsmath}
\usepackage[lite]{mtpro2}
\usepackage{systeme,regexpatch}
\makeatletter
% change the definition of \sysdelim not to store `\left` and `\right`
\def\sysdelim#1#2{\def\SYS@delim@left{#1}\def\SYS@delim@right{#2}}
\sysdelim\{. % reinitialize
% patch the internal command to use
% \LEFTRIGHT<left delim><right delim>{<system>}
% instead of \left<left delim<system>\right<right delim>
\regexpatchcmd\SYS@systeme@iii
{\cB.\c{SYS@delim@left}(.*)\c{SYS@delim@right}\cE.}
{\c{SYS@MT@LEFTRIGHT}\cB\{\1\cE\}}
{}{}
\def\SYS@MT@LEFTRIGHT{%
\expandafter\expandafter\expandafter\LEFTRIGHT
\expandafter\SYS@delim@left\SYS@delim@right}
\makeatother
\begin{document}
\[
\systeme{2x+3y=5,x-4y=-3}
\quad
\systeme[xzy]{2x+3y-z=5,x+2z-4y=-3,x+y=2}
\]
\end{document}
A \phantom helps make it work. Note I adjusted the notations of the second example to match those of the first, so that one can see the alignment matches up.
\documentclass[10pt]{amsart}
\usepackage{amsmath, amssymb, amsfonts, amsthm}
\usepackage{systeme}
\begin{document}
\title{Title}
\author{Author}
\date{\today}
\maketitle
\noindent Here is a system of linear equations whose solution is shown:
\[
\systeme[xyz]{x \phantom{{}+{}} - z = 1, y + 2z = 3, z = 0}
\quad \longrightarrow \quad
\systeme*[xyz]{x = 1, y = 3, z = 0}
\quad \longrightarrow \quad
\text{point $(1,1,0)$.}
\]
The $x$ and $y$ on the left side are too close. Compare it to this system:
\[
\systeme[xyz]{x + y - z = 1, y + 2z = 3, z = 0}
\quad \longrightarrow \quad
% \systeme*[xyz]{x = -2, y = 3, z = 0}
\systeme*[xyz]{x = 1, y = 3, z = 0}
\quad \longrightarrow \quad
\text{point $(1,1,0)$.}
% \text{point $(-2,1,0)$.}
\]
\end{document}
Best Answer
How about consecutive
\systemedirectives?The required amount of kerning between the
\systemeblocks will depend on both the font size and the math and text fonts that are in use. For Computer Modern and a 12pt document font size,\kern-26ptlooks "about right". If one were to load thenewtxtextandnewtxmathfont packages, then\kern-22ptwould be "about right".