An error in aligning several systems of linear equations using systeme

Question

I have code to typeset four systems of linear equations. I have all the equations aligned at the equals sign. In the first equation of the second system, I have

+ 0 = (q-m)x + b_{1},

but I want

0 = (q-m)x + b_{1},

and in the second equation of the second system, I have a gap between y and the equals sign. In the first equation of the third and fourth systems, there is a gap between x and the equals signs.

Also, I would like to add a comma after the first three systems of equations and a period after the last system of equations. I understand that , indicates a new equation within a \systeme command. So, I couldn't use , to have LaTeX typeset a comma within this environment. Anyway, I would want these punctuation marks centered between the two lines in each system of equations.

\documentclass{amsart}
\usepackage{mathtools,systeme,array}


\begin{document}

\begin{align*}
\systeme{y = \mathrlap{qx + b_{1}}, y = \mathrlap{mx}} \\
\systeme{0 = \mathrlap{(q - m)x + b_{1}}, y = \mathrlap{mx}} \\
\systeme{x = \mathrlap{\dfrac{b_{1}}{m - q}}, y = \mathrlap{mx}} \\
\systeme{x = \mathrlap{\dfrac{b_{1}}{m - q}}, y = \mathrlap{\dfrac{mb_{1}}{m - q}}} 
\end{align*}

\end{document}

Answer 1

Instead of using four systeme environments, you could use four array environments embedded in an align* environment.

\documentclass{amsart}
\begin{document}

\begin{align*}
&\bigg\{ \begin{array}{r @{{}={}} l}
y & qx + b_{1}\\y & mx 
\end{array},\\
&\bigg\{ \begin{array}{r @{{}={}} l}
0 & (q - m)x + b_{1}\\y & mx 
\end{array},\\
&\bigg\{ \begin{array}{r @{{}={}} l}
x & b_{1}/(m - q)\\y & mx
\end{array},\\
&\bigg\{ \begin{array}{r @{{}={}} l}
x & b_{1}/(m - q)\\y & mb_{1}/(m - q)
\end{array} .
\end{align*}

\end{document}

---

Addendum: Per your requst, here's a version of the system of equations that uses \dfrac macros instead of inline fractions for the final two systems. Because the curly braces in systems 3 and 4 are larger than those in systems 1 and 2, further horizontal spacing adjustments are also required to align the = symbols. (The need to perform horizontal spacing adjustments arises irrespective of whether array or systeme* environments are used.)

\documentclass{amsart}
\usepackage{mleftright} % "\mleft\{" avoids some spacing issues caused by "\left\{"
\begin{document}

\begin{align*}
&\bigg\{ \begin{array}{r @{{}={}} l}
y & qx + b_{1}\\y & mx 
\end{array},\\
&\bigg\{ \begin{array}{r @{{}={}} l}
0 & (q - m)x + b_{1}\\y & mx 
\end{array},\\
&\Bigg\{ \mkern-1.7mu \begin{array}{r @{{}={}} l}
x & \dfrac{b_{1}}{m - q}\\[1.5ex]y & mx
\end{array},\\
&\mleft\{ \mkern-3.2mu\begin{array}{r @{{}={}} l}
x & \dfrac{b_{1}}{m - q}\\[2.5ex] y & \dfrac{mb_{1}}{m - q}
\end{array} \mright. \,.
\end{align*}

\end{document}

---

Second Addendum: If you really don't want to eyeball-adjust the horizontal alignment of the large curly braces relative to their associated two-line systems of equations (each of which is placed in an array environment), I can only suggest you place the four arrays in the right-hand column of an "outer" two-column array: The left-hand column then contains the associated curly braces, sized via \vphantom directives.

\documentclass{amsart}
\usepackage{mleftright,array}

\begin{document}
%% First, define the four systems as arrays
\def\sysa{\begin{array}{r @{{}={}} l}
             y & qx + b_{1}\\y & mx 
          \end{array}}
\def\sysb{\begin{array}{r @{{}={}} l}
             0 & (q - m)x + b_{1}\\y & mx 
          \end{array}}
\def\sysc{\begin{array}{r @{{}={}} l}
             x & \dfrac{b_{1}}{m - q}\\[1.5ex] y & mx
          \end{array}}
\def\sysd{\begin{array}{r @{{}={}} l}
             x & \dfrac{b_{1}}{m - q}\\[2.5ex] y & \dfrac{mb_{1}}{m - q}
          \end{array}}

%% Second, place the systems in the right-hand column of an "outer" array
%% Each system array is featured twice: Inside a \vphantom statement in
%% the left-hand column, to determine the size of the curly brace, and 
%% again in the right-hand column as itself.
\[
\begin{array}{l@{}l}
    \mleft\{ \vphantom{\sysa} \mright. & \sysa \\[2.5ex]
    \mleft\{ \vphantom{\sysb} \mright. & \sysb \\[2.5ex]
    \mleft\{ \vphantom{\sysc} \mright. & \sysc \\[3.8ex]
    \mleft\{ \vphantom{\sysd} \mright. & \sysd 
\end{array}
\]

\end{document}

Answer 2

You want to use \systeme*, which doesn't do alignment. For the second, you also have to declare 0 as a variable. In the ones with the fraction I added a supplementary vertical spacing.

\documentclass{amsart}
\usepackage{systeme}

\begin{document}

\begin{align*}
&\systeme*{y = qx + b_{1}, y = mx} \\
&\systeme*[var=x,y,0]{0 = (q - m)x + b_{1}, y = mx} \\
&\syslineskipcoeff{1.75}\systeme*{x = \dfrac{b_{1}}{m - q}, y = mx} \\
&\syslineskipcoeff{1.75}\systeme*{x = \dfrac{b_{1}}{m - q}, y = \dfrac{mb_{1}}{m - q}}
\end{align*}

\end{document}

You can improve the spacing and add punctuation (but I'd avoid commas and periods); for a comma, place it in braces, so it will be invisible to the equation scanner.

\documentclass{amsart}
\usepackage{systeme}

\begin{document}

\begin{align*}
&\systeme*{y = qx + b_{1}, y = mx{\;,}} \\
&\systeme*[var=x,y,0]{0 = (q - m)x + b_{1}, y = mx{\;,}} \\
&\syslineskipcoeff{1.75}\systeme*{x = \dfrac{b_{1}}{m - q}, y = mx{\;,}} \\
&\syslineskipcoeff{2.25}\systeme*{x = \dfrac{b_{1}}{m - q}, y = \dfrac{mb_{1}}{m - q}{\;.}}
\end{align*}

\end{document}