Best way to arrange several (systems of) equations (of different size)

Question

There are many many examples of how to deal with and depict a system of (linear) equations (e.g. compare Best way to create an system of equations environment? ). But I like to design exercise sheets which contain several systems of equations, different in number of lines and probably very different in width.

I once asked a similar questions about the design for single equation lines, which workes in most cases (Start inparaenum-numeration with another letter than "a)" inparamenum function).

I would be able to do individual arrangements with several minipages.

\begin{align*}
  3x - 4y &= 7 \\
    x + 3y &= 11
\end{align*}

\begin{align*}
  (x+2)^2 + (y-1)^2 &= x^2 + y^2 + 1
\end{align*}

\begin{align*}
  \frac{2}{x-3y} + \frac{3}{2x+y} &= 2 \\
    \frac{8}{x-3y} - \frac{9}{2x+y} &= 1
\end{align*}

\begin{align*}
  4x + 2y - 3z &= 1 \\
    6x + 3y - 5z &= 0 \\
    x + y + 2z &= 9 
\end{align*}

I'm looking for a way to arrange those systems in maybe 2-4 column. Would be nice if the environment would be flexible on that, i.e. it chooses # of columns depending on the size of the system. Furthermore I need a numeration for each system (e.g. a, b, c, ...).

What is the best way of alignment for systems of equations?

Answer 1

You can do that either with the tasks package, or with shortlst, a small package that is not in TeX Live nor MiKTeX for licensing reasons, bur can de found on CTAN.

If an item is longer than one column, you can use the \tasks* command (it will use the remaining columns, or you can specify the number of columns you wish as an optional argument°. With shortlst, it automatically use the necessary columns.

\documentclass{article}

\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{systeme}
\usepackage{tasks}
\usepackage[showframe, nomarginpar]{geometry}
\newcommand\mystrut[1]{\rule{0pt}{#1}}
\settasks{counter-format=tsk[a])}
\usepackage{shortlst,setspace,xkeyval}%
\makeatletter
\newcounter{ncol}
\define@key{lex}{nc}[3]{\setcounter{ncol}{#1}}%% 3 columns by default
\define@key{lex}{il}[1]{\def\@intln{#1}}% interlining![1]
\newenvironment{tabenumerate}[1][]{%
\setkeys{lex}{nc,il,#1}
\settowidth{\labelwidth}{\mbox{(m)}}
\setlength{\leftmargini}{\dimexpr\labelwidth+\labelsep\relax}%[1][3]
\setlength{\shortitemwidth}{\dimexpr\linewidth/\value{ncol}-\labelwidth-2\labelsep\relax}%
\renewcommand{\labelenumi}{\ensuremath{\arabic{enumi}.}}
\setstretch{\@intln}
\begin{shortenumerate}}%
{\end{shortenumerate}
}%
\newcommand\paritem[2][1]{\item \parbox[t]{#1\shortitemwidth}{\setstretch{1}#2\medskip}}
\makeatother

\begin{document}

\noindent Solve the following (systems of) equations:
\begin{tasks}(3)
  \task \systeme{-3x-4y = 7, x + 3y = 11}
  %
  \task*$ (x+2)^2 + (y-1)^2 = x^2 + y^2 + 1 $
  %
  \task $ \left\{\begin{aligned}
  \frac{2}{x-3y} + \frac{3}{2x+y} &= 2 \\
  \frac{8}{x-3y} - \frac{9}{2x+y} &= 1
  \end{aligned}\right. $
  %
  \task \systeme{ 4x + 2y - 3z = 1, 6x + 3y - 5z = 0, x + y + 2z = 9}
  %
  \task $\sin2\theta = \cos 5\theta$
\end{tasks}
\bigskip

\noindent Solve the following (systems of) )equations:
\begin{tabenumerate}
  \renewcommand\labelenumi{\alph{enumi})}
  \item$ \systeme{-3x-4y = 7, x + 3y = 11} $
  %
  \item $ (x+2)^2 + (y-1)^2 = x^2 + y^2 + 1 $
  %
  \item \mystrut{8ex}$\left\{\begin{aligned}
  \frac{2}{x-3y} + \frac{3}{2x+y} &= 2 \\
  \frac{8}{x-3y} - \frac{9}{2x+y} &= 1
  \end{aligned}\right.$
  %%
  \item $\systeme{
    4x + 2y - 3z = 1,
    6x + 3y - 5z = 0,
    x + y + 2z = 9}$
  %
  \item $\sin2\theta = \cos 5\theta$
\end{tabenumerate}

\end{document} %