# Write several systems of linear equations in one line

How to write several systems of linear equations in one line with automatic transfer?

\begin{multline*}
\begin{split}
\begin{cases}
- x + 8y = -15\\
4x -4y = 32\\
\end{cases}
\end{split}
\end{multline*}
%
\begin{multline*}
\begin{split}
\begin{cases}
y = \cfrac{x-15}{8}\\
4x -4y = 32\\
\end{cases}
\end{split}
\end{multline*}
%
\begin{multline*}
\begin{split}
\begin{cases}
y = \cfrac{x-15}{8}\\
4x -4(\cfrac{x-15}{8}) = 32\\
\end{cases}
\end{split}
\end{multline*}
%
\begin{multline*}
\begin{split}
\begin{cases}
y = \cfrac{x-15}{8}\\
7x = 49\\
\end{cases}
\end{split}
\end{multline*}
%
\begin{multline*}
\begin{split}
\begin{cases}
y = -1\\
x = 7\\
\end{cases}
\end{split}
\end{multline*}
%


I want to write down several systems of linear equations so that they go from left to right, top to bottom (an example of solving a system of linear equations), and not one under the other (by default).

• Welcome to TeX.SE!
– user156344
Apr 2, 2019 at 8:58

Still another solution, which employs five side-by-side array environments.

\documentclass{article}
\usepackage[letterpaper,margin=1in]{geometry}
\usepackage{array}

\newcommand\myarray[1]{%
\begingroup
\renewcommand\arraystretch{1.33}
\left\{ \begin{array}{@{}l@{}} #1 \end{array} \right.
\endgroup}

\begin{document}
$\myarray{-x + 8y = -15\\4x -4y = 32} \Rightarrow \myarray{y = \frac{1}{8}(x-15)\\4x -4y = 32} \Rightarrow \myarray{y = \frac{1}{8}(x-15)\\4x -\frac{4}{8}(x-15) =32} \Rightarrow \myarray{y = \frac{1}{8}(x-15)\\7x = 49} \Rightarrow \myarray{y = \frac{1}{8}(-8)=-1\\x = 7}$
Alternatively, without any \verb+\frac+ terms:
$\myarray{-x + 8y = -15\\4x -4y = 32} \Rightarrow \myarray{-x + 8y = -15\\x = 8+y} \Rightarrow \myarray{-8-y+8y=-15\\x = 8+y} \Rightarrow \myarray{7y=-7\\x = 8+y} \Rightarrow \myarray{y = -1\\x = 8+(-1)=7}$
\end{document}


Here's my proposal for automatic breaking:

\documentclass{article}
\usepackage{amsmath}

\newenvironment{multisys}
{\begin{minipage}{\displaywidth}
\lineskip=1ex
\leftskip=0pt plus 1fil
\rightskip=.15\displaywidth plus 1fill
\parfillskip=-.15\displaywidth plus -1fill
$} {$\end{minipage}}

\newenvironment{system}
{\left\lbrace\renewcommand{\arraystretch}{1.2}\begin{array}{@{}l@{}}}
{\end{array}\right.\kern-\nulldelimiterspace}

\begin{document}

$\begin{multisys} \begin{system} - x + 8y = -15\\[2ex] 4x -4y = 32 \end{system} \iff \begin{system} y = \dfrac{x-15}{8}\\[2ex] 4x -4y = 32 \end{system} \iff \begin{system} y = \dfrac{x-15}{8}\\[2ex] 4x -4\left(\dfrac{x-15}{8}\right) = 32 \end{system} \iff \begin{system} y = \dfrac{x-15}{8}\\[2ex] 7x = 49 \end{system} \iff \begin{system} y = -1\\[2ex] x = 7 \end{system} \end{multisys}$

\end{document}


Try to use it:

\left \{
\begin{tabular}{ccc}
- x + 8y = -15\\
4x -4y = 32\\
\end{tabular}
\Rightarrow
\left \{
\begin{tabular}{ccc}
- x + 8y = -15\\
4x -4y = 32\\
\end{tabular}


Resource here.

If you want to use displaystyle fractions, use \dfrac. \cfrac is for continuous fractions. However, I prefer medium-sized fraction, \mfrac, which comes from nccmath.

Like this?

\documentclass{article}
\usepackage{mathtools}
\usepackage{nccmath}
\begin{document}
\begin{multline*}
\left\{\begin{matrix*}[l]
- x + 8y = -15\\
4x -4y = 32\\
\end{matrix*}\right.\Leftrightarrow\left\{\begin{matrix*}[l]
y = \mfrac{x-15}{8}\\[1ex]
4x -4y = 32\\
\end{matrix*}\right.\\
\Leftrightarrow\left\{\begin{matrix*}[l]
y = \mfrac{x-15}{8}\\[1ex]
4x -4\left(\mfrac{x-15}{8}\right) = 32\\
\end{matrix*}\right.\Leftrightarrow\left\{\begin{matrix*}[l]
y = \mfrac{x-15}{8}\\[1ex]
7x = 49\\
\end{matrix*}\right.\Leftrightarrow\left\{\begin{matrix*}[l]
y = -1\\
x = 7\\
\end{matrix*}\right.
\end{multline*}
\end{document}


Recommended approach:

\documentclass{article}
\usepackage{mathtools}
\usepackage{nccmath}
\begin{document}
\begin{align*}
\left\{\begin{matrix*}[l]
- x + 8y = -15\\
4x -4y = 32\\
\end{matrix*}\right.&\Leftrightarrow\left\{\begin{matrix*}[l]
y = \mfrac{x-15}{8}\\[1ex]
4x -4y = 32\\
\end{matrix*}\right.\\
&\Leftrightarrow\left\{\begin{matrix*}[l]
y = \mfrac{x-15}{8}\\[1ex]
4x -4\left(\mfrac{x-15}{8}\right) = 32\\
\end{matrix*}\right.\\
&\Leftrightarrow\left\{\begin{matrix*}[l]
y = \mfrac{x-15}{8}\\[1ex]
7x = 49\\
\end{matrix*}\right.\\
&\Leftrightarrow\left\{\begin{matrix*}[l]
y = -1\\
x = 7\\
\end{matrix*}\right.
\end{align*}
\end{document}