Error message while making a linear equation system equation using systeme

Question

I've been trying to make a system of linear equations in LaTeX for a while, I couldn't even find results on the internet. Another thing to note is everything I've tried was based on the \systeme command provided by the systeme package that everyone seems to use, I don't know if there's a better alternative to that I could use but if there is, I'd be very happy to know. I'll use this equation as an example:

x-y=1
x^{2}+y^{2}=41

By solving this equation I get to

\systeme{x-y=1, x^{2}+y^{2}=41} 
\systeme{x=y+1,x^{2}+y^{2}=41} 
\systeme{x=y+1,(y+1)^{2}+y^{2}} 

All the codes until \systeme{x=y+1,(y+1)^{2}+y^{2}} work fine, but that one really doesn't work, I've tried various different things but it always displays this error message in french

! Package systeme Error: l'inconnue "y_{-1}" a deja ete trouvee dans l'equation
 !.
<argument> ... deja ete trouvee dans l'equation !}
                                                  \fi \ifSYS_sortvariable \S...
l.78 \systeme{x=y+1,(y+1)^{2}+y^{2}}

I don't know french but by putting it in google translate I get:

! Package system Error: the unknown "y _ {- 1}" has already been found in the equation
 !
<argument> ... already found in the equation!}
                                                  \ fi \ ifSYS_sortvariable \ S ...
l.78 \ system {x = y + 1, (y + 1) ^ {2} + y ^ {2}}

I think the problem is that y appeared twice in the equation, but that is supposed to happen, is there anything I could do besides putting y_{1} and y_{2} in the entire equation? Thanks in advance

Answer 1

I see no sensible way to align variables in nonlinear systems. Maybe the first system might have x and y aligned with each other, but what about the other two?

\documentclass{article}
\usepackage{amsmath,array}

\newenvironment{lsystem}% left aligned system
 {\left\lbrace\renewcommand{\arraystretch}{1.2}\begin{array}{@{}l@{}}}
 {\end{array}\right.}

\begin{document}

\[
\begin{lsystem}
x-y=1 \\
x^2+y^2=41
\end{lsystem}
\quad
\begin{lsystem}
x=y+1 \\
x^2+y^2=41
\end{lsystem}
\quad
\begin{lsystem}
x=y+1 \\
(y+1)^2+y^2=41
\end{lsystem}
\]

\end{document}

Why not cases? Because it would add unwanted space at its right side.