# How to subtract two equations?

I am trying to subtract one equation from another but I can't get it to display the way that I want. This is what I have right now.

\begin{align*}
&y&=2x+5\\
-&&\\
&y&=3x+10\\\hline
&0&=-x-5
\end{align*}

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Well, how do you want it to display? – Ryan Reich Feb 1 '12 at 19:22
Is this to demonstrate solving linear equations by addition? If so, why not multiply the bottom equation by -1 and present it as addition as you have it: (a la purplemath.com/modules/systlin5.htm). – badroit Feb 1 '12 at 19:26
It looks like this began life as an eqnarray. Try loosing the second & on each line just to start with. – qubyte Feb 1 '12 at 19:27

This does not look very good but seems close to what your code is attempting to do, where I use \cline{} to draw the horizontal line, and \phantom{y=} to push the minus sign to the left

## Recomended Solution:

However, I would suggest the use of \intertext or \shortintertext from the mathtools package, and refer to the equations:

## Notes:

• Requires two runs: first run will display a (??) in the cross reference.
• \shortintertext yields better spacing but requires an additional package. Alternatively, you can use \intertext which is available in amsmath.
• The mathtools package already includes amsmath.

## Code:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
y&=2x+5\\
-\phantom{y=}&\\
y&=3x+10\\
\cline{1-2}
0&=-x-5
\end{align*}
\end{document}


\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{align}
y&=2x+5 \label{eqn:one}\\
y&=3x+10 \label{eqn:two}\\
\shortintertext{Subtracting \eqref{eqn:two} from \eqref{eqn:one} yields}
0&=-x-5  \notag
\end{align}
\end{document}

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+1 for the recommended version :-) – Tobi Feb 1 '12 at 21:59
The recommended version is indeed much better in my opinion. A small nitpick: \eqref might be better to make a distinction between numbers and equations. – percusse Feb 1 '12 at 22:07
Seeing your recommended version, I think that it is a better approach. – russjohnson09 Feb 1 '12 at 23:36
@percusse: Thanks for pointing that out. Have updated the solution to correct that. – Peter Grill Feb 2 '12 at 0:34

My two-cents worth, using more of a textual representation and an array:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
$\begin{array}{l@{\quad}cr@{}l} && y & {}= 2x+5 \\ \text{minus} && y & {}= 3x+10 \\ \cline{2-4} && 0 & {}= -x-5 \end{array}$
\end{document}​


The additional (second) column is to allow for the \cline to have a little padding around the equations. Modify \quad to \hspace{<len>} to have a gap of length <len> between "minus" and the equation.

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Here is my solution:

\documentclass[]{article}

\usepackage{amsmath}
\begin{document}
\begin{alignat*}{4}
&y&=&&2x&&+&5\\
-\hspace*{.5em}&y&=&&3x&&+&10\-2.5ex]\cline{2-8}\\[-4.8ex] &0&=&&-x&&-&5 \end{alignat*} \end{document}  I use the alignat enviroment from amsmath - Good one. Your spacing around the = on the second line is wrong. try removing the first & on each line. Hmmmm, on second thought, the location of the minus sign means "negative y", not minus the entire equation... – Peter Grill Feb 1 '12 at 20:03 I already noted the problem. and posted the corrected version. thx ;) – someonr Feb 1 '12 at 20:05 Actually you should just use a single & to get the proper math spacing. Still there is a problem with the meaning of "minus y", which is not the OP's intent. – Peter Grill Feb 1 '12 at 20:07 Yeah ok. I fixed it... But I'm not sure what russjohnson09 would like to see – someonr Feb 1 '12 at 20:20 I write it like this: \[\frac{\begin{matrix} y=2x+5\\ y=3x+10 \end{matrix}}{0=-x-5}\ -

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Stealing the idea with \frac from this answer but replacing the matrix with aligned. Is it a cute idea? I hope so!

\documentclass[preview,border=12pt,varwidth]{standalone}

\usepackage{amsmath}
\begin{document}
\abovedisplayskip=0pt\relax
\frac { \!\begin{aligned} y &= 2x+5\\ y &= 3x+10 \end{aligned} } {0=-x-5} \ -
\end{document}


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