Math & Science ⇒ System of equations

[solunac]

Hi!

I am stuck with system of linear equations. I need to put them aligned so that it looks like this:


I wrote a code (but wrong) so you can work with it.

Code: Select all

\begin{align*}
x_0           &+\frac{7}{22}x_3 &+\frac{5}{22}x_4      &= \frac{21}{2}\\
    &x_1      &+\frac{3}{22}x_3 &-\frac{1}{22}x_4      &= \frac{7}{2}\\
         &x_2 &+\frac{1}{22}x_3 &+\frac{7}{22}x_4      &= \frac{7}{2}\\
              &\frac{3}{2}x_3   &+\frac{5}{2}x_4 &+x_5 &= \frac{55}{2}.
\end{align*}

Thanks in advance.

[frabjous]

Align and similar environments will always put something right aligned next to something left aligned, as in an equation, but you want something more complicated than that. All parts are left or center aligned. I guess I might try an array. E.g.:

Code: Select all

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\begin{array}{cccllllc}
x_0 &    &    &+\frac{7}{22}x_3 &+\frac{5}{22}x_4 &     &=&\frac{21}{2}\\[1ex]
    &x_1 &    &+\frac{3}{22}x_3 &-\frac{1}{22}x_4 &     &=&\frac{7}{2}\\[1ex]
    &    &x_2 &+\frac{1}{22}x_3 &+\frac{7}{22}x_4 &     &=&\frac{7}{2}\\[1ex]
    &    &    &+\frac{3}{2}x_3   &+\frac{5}{2}x_4  &+x_5 &=&\frac{55}{2}.
\end{array}
\end{equation*}
\end{document}

[solunac]

Thanks, one more time!

[localghost]

Just for the record. The alignment done with alignat environment.

Code: Select all

\documentclass[11pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}

\allowdisplaybreaks

\begin{document}
  \begin{alignat*}{6}
    x_0 &    &&    &&+\tfrac{7}{22}x_3      &&+\tfrac{5}{22}x_4 &&     &&= \tfrac{21}{2} \\
        &x_1 &&    &&+\tfrac{3}{22}x_3      &&-\tfrac{1}{22}x_4 &&     &&= \tfrac{7}{2} \\
        &    &&x_2 &&+\tfrac{1}{22}x_3      &&+\tfrac{7}{22}x_4 &&     &&= \tfrac{7}{2} \\
        &    &&    &&\quad\,\tfrac{3}{2}x_3 &&+\tfrac{5}{2}x_4  &&+x_5 &&= \tfrac{55}{2}
  \end{alignat*}
\end{document}

Not exactly what you want, but wouldn't cause trouble if it comes to a page break. Horizontal spaces can be customized.


Best regards and welcome to the board
Thorsten

[azoun]

here it is my solution

Code: Select all

\begin{equation*}
\begin{array}{cccllllc}
x_0 &    &    &+\frac{7}{22}x_3 &+\frac{5}{22}x_4 &     &=&\frac{21}{2}\\[1ex]
    &x_1 &    &+\frac{3}{22}x_3 &-\frac{1}{22}x_4 &     &=&\frac{7}{2}\\[1ex]
    &    &x_2 &+\frac{1}{22}x_3 &+\frac{7}{22}x_4 &     &=&\frac{7}{2}\\[1ex]
    &    &    &+\frac{3}{2}x_3   &+\hfill\frac{5}{2}x_4  &+x_5 &=&\frac{55}{2} %<---HERE
\end{array}
\end{equation*}

I prefer so

Code: Select all

\begin{equation*}
\begin{array}{cccllllc}
x_0 &    &    &+\frac{7}{22}x_3 &+\frac{5}{22}x_4 &     &=&\frac{21}{2}\\[1ex]
    &x_1 &    &+\frac{3}{22}x_3 &-\frac{1}{22}x_4 &     &=&\frac{7}{2}\\[1ex]
    &    &x_2 &+\frac{1}{22}x_3 &+\frac{7}{22}x_4 &     &=&\frac{7}{2}\\[1ex]
    &    &    &+\frac{3}{2}x_3   &+\hfill\frac{5}{2}x_4  &+x_5 &=&\frac{55}{2}%<---HERE
\end{array}
\end{equation*}

[tonyjnel]

This is almost what I am looking for but there is too much space between the elements of the array. I want mine to read just like an equation (like the rest of my equations that aren't arrays) so that my paper is consistent. I tried this:

Code: Select all

\begin{align*}
5x_1&+3x_2&+x_3&=0\\
x_1&+{}&-4x_3&=0\\
{}&-9x_2&+2x_3&=0\end{align*}

and the first two terms look great but then there is a huge gap between the next ones.

Thanks,
Tony

[Stefan Kottwitz]

Hi Tony,

you could use the alignat* environment. It allows alignment at several places. A mandatory argument specifies the number of columns. For example:

Code: Select all

\begin{alignat*}{2}
5x_1 &+ 3x_2 &&+ x_3  &= 0\\
 x_1 &+      &&- 4x_3 &= 0\\
     &- 9x_2 &&+ 2x_3 &= 0
\end{alignat*}

Stefan

[tonyjnel]

Thanks Stefan! That is exactly what I wanted. I think there were some typos in your code though.. LaTeX didn't give me errors when I changed it to

Code: Select all

\begin{alignat*}{4}
5x_1 &+ 3x_2 &+ x_3  &= 0\\
x_1 &+      &- 4x_3 &= 0\\
     &- 9x_2 &+ 2x_3 &= 0
\end{alignat*}

-Tony

[Juanjo]

In my opinion, your code generates a system of equations with some flaws: there is a superfluous + sign in the second row, signs are not vertically aligned, the spacing around signs is not correct...
Please, try this:

Code: Select all

\begin{alignat*}{3}
  5x_1 &+{}& 3x_2 &+{}&  x_3 &= 0 \\
   x_1 &   &      &-{}& 4x_3 &= 0 \\
       &-{}& 9x_2 &+{}& 2x_3 &= 0
\end{alignat*}

The mandatory argument of alignat is the number of «columns» in the aligned formulas (in this case, one column for each variable x_i; the third and last column also contains the independent terms). Two consecutive columns are separated by an ampersand (&). In each column, the alignment point is also marked by an ampersand. So, if there are n columns, there should be 2n-1 ampersands per row. In every row, the first ampersand marks the aligment point for the first column; the second ampersand marks the end of the first column; the third ampersand marks the alignment point for the second column; and so on.

[unbonpetit]

Can I suggest the use of the "systeme" package:

Code: Select all

\documentclass{minimal}
\usepackage{systeme}
\begin{document}
My system:
\systeme{x_0+\frac{7}{22}x_3+\frac{5}{22}x_4=\frac{21}{2},
x_1+\frac{3}{22}x_3-\frac{1}{22}x_4=\frac{7}{2},
x_2+\frac{1}{22}x_3+\frac{7}{22}x_4=\frac{7}{2},
\frac{3}{2}x_3+\frac{5}{2}x_4+x_5=\frac{55}{2}}

Another one:
\systeme{5x_1+3x_2+x_3=0,
x_1-4x_3=0,
-9x_2+2x_3=0}
\end{document}