4

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}
3

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

enter image description here

\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.)

enter image description here

\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.

enter image description here

\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}
  • I prefer your code. May you give it to me with the the quotients typeset using the \dfrac commands? – Adelyn May 26 '15 at 18:44
  • 1
    @Adelyn - Done. Note that the use of \dfrac instead of inline fractions requires both vertical as well as horizontal spacing adjustments -- that's why I had posted the inline fraction version first... :-) – Mico May 26 '15 at 19:08
  • 1
    @Adelyn - On the horizontal spacing adjustments: The first three systems involve \bigg and \Bigg left curly braces, which do not insert whitespace on their left; that's why I suggest using \mleft\{ rather than \left\{ for the curly brace for system 4. Because the curly braces in systems 3 and 4 are taller than those in systems 1 and 2, they are also a bit wider, requiring some adjustment on their right. The adjustment directives \mkern-1.7mu and \mkern-3.2mu -- \mkern-3mu is equivalent to \!, by the way -- were chosen by eyeballing the results. – Mico May 27 '15 at 3:38
  • 1
    @Adelyn - For what it's worth, if you look closely at both of egreg's solutions, you'll notice that the = symbols in systems 3 and 4 are not perfectly aligned with those in systems 1 and 2; this is a consequence of the fact that the curly braces in systems 3 and 4 are (slightly) wider than those in systems 1 and 2. An spacing adjustment somewhere between \mkern-1.5mu and \mkern-2mu would seem necessary to bring about alignment of all four = symbols. – Mico May 27 '15 at 3:44
  • 1
    @Adelyn - I don't think your idea (of avoiding eyeball-based horizontal adjustments) can be accomplished along the lines you suggest. I've edited my answer to provided a second addendum, in which I show how the idea may be implemented using nested array environments. – Mico May 28 '15 at 4:13
4

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}

enter image description here

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}

enter image description here

  • The two \dfracs in the final systeme* seem awfully close to each other. – Mico May 26 '15 at 18:22
  • @egreg That is (almost) the display that I wanted. How do I add the punctuation marks? – Adelyn May 26 '15 at 18:26
  • @egreg Are you saying that systeme aligns at the left brace? I think that I tried using it and there was no alignment with the left brace. – Adelyn May 26 '15 at 18:28
  • @egreg You use \syslineskipcoeff{1.75} in both the third and fourth systems of linear equations. The line separations appear differently, though. – Adelyn May 26 '15 at 18:31
  • 1
    @Adelyn I don't know where the commas should be placed, so I didn't add them. The systems are left aligned because of the & that precedes each one. The separation is the same in the last two systems, but the fourth has a taller second equation; increase the value. – egreg May 26 '15 at 19:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.