Here are two possibilities, depending on what you mean by "curly".
The first type of brace grows wider the taller it gets; however, in this case, I have limited its maximum width to 3ex.
The second type of brace will never grow wider, but only taller.
EDITED to add \stackMath
to perform stacks in math mode.
\documentclass{article}
\usepackage{scalerel}
\usepackage[usestackEOL]{stackengine}
\stackMath
\begin{document}
\[
\scaleleftright[3ex]{\{}
{\Centerstack{a=x+2y+3z\\
b=6x+y+2z\\
c=5x+3y+z}}
{\}}
\quad
\left\{
\Centerstack{a=x+2y+3z\\
b=6x+y+2z\\
c=5x+3y+z}
\right \}
\]
\end{document}

If you had a curly-brace glyph that was more to your liking from a different (importable) font, it could be used in the first method presented below.
For example, here we use the brace from the mathdesign
package.
\documentclass{article}
\usepackage{scalerel}
\usepackage[usestackEOL]{stackengine}
\stackMath
\usepackage[utopia]{mathdesign}
\begin{document}
\[
\scaleleftright[3ex]{\{}
{\Centerstack{a=x+2y+3z\\
b=6x+y+2z\\
c=5x+3y+z}}
{\}}
\quad
\left\{
\Centerstack{a=x+2y+3z\\
b=6x+y+2z\\
c=5x+3y+z}
\right \}
\]
\end{document}

As a follow up for the OP, the mathdesign
braces may be solely obtained (as \textbraceleft
and \textbraceright
) using the method of egreg at Import curly brackets from MathDesign (Utopia).
In the MWE below, I only import it as such. So the left hand \scaleleftright
uses it, while the right-hand solution uses the default LaTeX brace. However, by uncommenting the additional code provided, these curly braces will become the default math brace.
In either case, however, the rest of the mathdesign
glyphs are not imported.
\documentclass{article}
\usepackage{scalerel}
\usepackage[usestackEOL]{stackengine}
\stackMath
%\usepackage[utopia]{mathdesign}
\DeclareSymbolFont{mdsymbols} {OMS}{mdput}{m}{n}
\DeclareSymbolFont{mdlargesymbols}{OMX}{mdput}{m}{n}
% TO GET ALL BRACES REPLACED WITH THE mathdesign BRACE
%\DeclareMathDelimiter{\lbrace}
% {\mathopen}{mdsymbols}{"66}{mdlargesymbols}{"08}
%\DeclareMathDelimiter{\rbrace}
% {\mathclose}{mdsymbols}{"67}{mdlargesymbols}{"09}
%
% TO JUST IMPORT mathdesign BRACES AS \textbraceleft and \textbraceright
\renewcommand{\textbraceleft}{%
{\fontfamily{mdput}\fontencoding{OMS}\selectfont\char"66}}
\renewcommand{\textbraceright}{%
{\fontfamily{mdput}\fontencoding{OMS}\selectfont\char"67}}
\begin{document}
\[
\scaleleftright[3ex]{$\textbraceleft$}
{\Centerstack{a=x+2y+3z\\
b=6x+y+2z\\
c=5x+3y+z}}
{$\textbraceright$}
\quad
\left\{
\Centerstack{a=x+2y+3z\\
b=6x+y+2z\\
c=5x+3y+z}
\right \}
\]
\end{document}
