Write several systems of linear equations in one line

Question

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).

Answer 1

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}

Answer 2

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}

Answer 3

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.

Answer 4

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}