System of linear equations wobbles

Question

I tried to illustrate how to solve a system of linear equations but I don't come along with the different approaches to position the equations. They are shifted at some slides, e.g. if an arrow is displayed or even if some variables are only colored!

Here's my simple but not so minimal looking example:

\documentclass[dvipsnames,mathserif]{beamer}

\usepackage{tikz}
\RequirePackage{color}
\usepackage{amsmath}

\newcommand{\ma}[1]{\textcolor[named]{Magenta}{#1}}
\newcommand{\cy}[1]{\textcolor[named]{Cyan}{#1}}

\begin{document}

\tikzstyle{every picture}+=[remember picture]

%%%%%%%% Folie  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame
{
  \frametitle{LGS (without anything)}
  %=========================== 
  \begin{alignat*}{4}
    x_1\    &+\ 2x_2\   &          &+\ x_4\     &=\ 1\\
    x_1\    &+\ 2x_2\   &+\ 2x_3\  &+\ 3x_4\    &=\ 5\\
    2x_1\   &+\ 4x_2\   &          &+\ 3x_4\    &=\ 5\\
            &           &  3x_3\   &+\ 2x_4\    &=\ 3
  \end{alignat*}


}

\frame
{
  \frametitle{LGS (with arrow)}
  %===========================
  \begin{alignat*}{5}
          &          &  3x_3\   &+\ 2x_4\   &=\ 3 &\tikz{\node (n1){};} \\
    x_1\  &+\ 2x_2\  &+\ 2x_3\  &+\ 3x_4\   &=\ 5 \\
    2x_1\ &+\ 4x_2\  &          &+\ 3x_4\   &=\ 5 \\
     x_1\ &+\ 2x_2\  &+\ x_4\   &=\ 1       &\tikz{\node (n2){};}
  \end{alignat*}

  \begin{tikzpicture}[overlay]
    \path<2>[blue,<->,thick] (n1.east) edge [out= 330, in= 30] (n2.east);
  \end{tikzpicture}  
}

%%%%%%%% Folie  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame
{
  \frametitle{LGS (colored variables and with arrow)}
  %===========================
  %\normalsize
  \begin{alignat*}{5}
              &               &\cy{3x_3}\  &+\ \cy{2x_4}\ &=\ \cy{3} &\tikz{\node (n3){};} \\
    x_1\      &+\ 2x_2\       &+\ 2x_3\    &+\ 3x_4\      &=\ 5 \\
    2x_1\     &+\ 4x_2\       &            &+\ 3x_4\      &=\ 5 \\
    \ma{x_1}\ &+\ \ma{2x_2}\  &            &+\ \ma{x_4}\  &=\ \ma{1} &\tikz{\node (n4){};}
  \end{alignat*}

  \begin{tikzpicture}[overlay]
    \draw[blue,<->,thick] (n3.east) to [out= 330, in= 30] (n4.east);
  \end{tikzpicture}
}

%%%%%%%% Folie  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame
{
  \frametitle{LGS (colored variables)}
  %===========================


  \begin{alignat*}{4}
    \ma{x_1}\ &+\ \ma{2x_2}\ &              &+\ \ma{x_4}\  &=\ \ma{1}\\
        x_1\  &+\ 2x_2\      &+\ 2x_3\      &+\ 3x_4\      &=\ 5 \\
       2x_1\  &+\ 4x_2\      &              &+\ 3x_4\      &=\ 5 \\
              &              &\cy{3x_3}\    &+\ \cy{2x_4}\ &=\ \cy{3} \\ 
  \end{alignat*}

}

\frame
{
  \frametitle{LGS (again without anything)}
  %=========================== 
  \begin{alignat*}{4}
    x_1\    &+\ 2x_2\       &          &+\ x_4\     &=\ 1\\
    x_1\    &+\ 2x_2\       &+\ 2x_3\  &+\ 3x_4\    &=\ 5\\
    2x_1\   &+\ 4x_2\       &          &+\ 3x_4\    &=\ 5\\
            &               &  3x_3\   &+\ 2x_4\    &=\ 3
  \end{alignat*}


}

\end{document}

Answer 1

In order to avoid the wobbling, you need to ensure that the content of each slide matchs with the others, and maintain a similar structure across the slides.

The horizontal wobbling is due to the fact that you are using a different number of alignment columns in the alignat. So adjusting those to all use the same number and adding a few \phantom fixes the problem.

The vertical wobbling can also be fixed by putting an empty tikxpicture:

  \begin{tikzpicture}
  \end{tikzpicture}  

Also, I would highly recommend that you eliminate the \ that you have manually placed to add additional spacing.

\documentclass[dvipsnames,mathserif]{beamer}

\usepackage{tikz}
\RequirePackage{color}
\usepackage{amsmath}

\newcommand{\ma}[1]{\textcolor[named]{Magenta}{#1}}
\newcommand{\cy}[1]{\textcolor[named]{Cyan}{#1}}

\begin{document}

\tikzstyle{every picture}+=[remember picture]

%%%%%%%% Folie  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame
{
  \frametitle{LGS (without anything)}
  %=========================== 
  \begin{alignat*}{5}
    x_1\    &+\ 2x_2\   &          &+\ \phantom{3}x_4\     &=\ 1 & \phantom{\tikz{\node (m1){};}}\\
    x_1\    &+\ 2x_2\   &+\ 2x_3\  &+\ 3x_4\    &=\ 5\\
    2x_1\   &+\ 4x_2\   &          &+\ 3x_4\    &=\ 5\\
            &           &  3x_3\   &+\ 2x_4\    &=\ 3
  \end{alignat*}
  \begin{tikzpicture}
  \end{tikzpicture}  
}

\frame
{
  \frametitle{LGS (with arrow)}
  %===========================
  \begin{alignat*}{5}
          &          &  3x_3\   &+\ 2x_4\   &=\ 3 &\tikz{\node (n1){};} \\
    x_1\  &+\ 2x_2\  &+\ 2x_3\  &+\ 3x_4\   &=\ 5 \\
    2x_1\ &+\ 4x_2\  &          &+\ 3x_4\   &=\ 5 \\
     x_1\ &+\ 2x_2\  &          &+\ \phantom{3}x_4\    &=\ 1 &\tikz{\node (n2){};}
  \end{alignat*}
  %
  \begin{tikzpicture}[overlay]
    \path<2>[blue,<->,thick] (n1.east) edge [out= 330, in= 30] (n2.east);
  \end{tikzpicture}  
}

%%%%%%%% Folie  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame
{
  \frametitle{LGS (colored variables and with arrow)}
  %===========================
  %\normalsize
  \begin{alignat*}{5}
              &               &\cy{3x_3}\  &+\ \cy{2x_4}\ &=\ \cy{3} &\tikz{\node (n3){};} \\
    x_1\      &+\ 2x_2\       &+\ 2x_3\    &+\ 3x_4\      &=\ 5 \\
    2x_1\     &+\ 4x_2\       &            &+\ 3x_4\      &=\ 5 \\
    \ma{x_1}\ &+\ \ma{2x_2}\  &            &+\ \phantom{3}\ma{x_4}\  &=\ \ma{1} &\tikz{\node (n4){};}
  \end{alignat*}
  %
  \begin{tikzpicture}[overlay]
    \draw[blue,<->,thick] (n3.east) to [out= 330, in= 30] (n4.east);
  \end{tikzpicture}
}

%%%%%%%% Folie  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame
{
  \frametitle{LGS (colored variables)}
  %===========================
  \begin{alignat*}{5}
    \ma{x_1}\ &+\ \ma{2x_2}\ &              &+\ \ma{\phantom{3}x_4}\  {}&=\ \ma{1}&\phantom{\tikz{\node (m2){};}}\\
        x_1\  &+\ 2x_2\      &+\ 2x_3\      &+\ 3x_4\                 &=\ 5 \\
       2x_1\  &+\ 4x_2\      &              &+\ 3x_4\                 &=\ 5 \\
              &              &\cy{3x_3}\    &+\ \cy{2x_4}\            &=\ \cy{3}
  \end{alignat*}
  \begin{tikzpicture}
  \end{tikzpicture}  
}

\frame
{
  \frametitle{LGS (again without anything)}
  %=========================== 
  \begin{alignat*}{5}
    x_1\    &+\ 2x_2\       &          &+\ \phantom{3}x_4\     &=\ 1&\phantom{\tikz{\node (m3){};}}\\
    x_1\    &+\ 2x_2\       &+\ 2x_3\  &+\ 3x_4\    &=\ 5\\
    2x_1\   &+\ 4x_2\       &          &+\ 3x_4\    &=\ 5\\
            &               &  3x_3\   &+\ 2x_4\    &=\ 3
  \end{alignat*}
  \begin{tikzpicture}
  \end{tikzpicture}  
}
\end{document}

---

As suggested by Werner, an alternate solution to avoid having to include the \phantom{\tikz{\node (n1){};}} is to enclose the actual nodes in an \rlap as follows:

  \begin{alignat*}{4}
              &               &\cy{3x_3}\  &+\ \cy{2x_4}\ &=\ \cy{3} \rlap{\quad \tikz{\node (n3){};}} \\
    x_1\      &+\ 2x_2\       &+\ 2x_3\    &+\ 3x_4\      &=\ 5 \\
    2x_1\     &+\ 4x_2\       &            &+\ 3x_4\      &=\ 5 \\
    \ma{x_1}\ &+\ \ma{2x_2}\  &            &+\ \ma{x_4}\  &=\ \ma{1} \rlap{\quad \tikz{\node (n4){};}}
  \end{alignat*}

Answer 2

A non-Tikz solution to building a system of linear equations a piece at a time (matrix form, but still generally applicable):

The code can probably be tightened up---I originally wrote it in 2004 (or possibly earlier), when I was just getting started on Beamer.

\documentclass{beamer}
\usepackage{amsmath}

\begin{document}

\frame{
  \frametitle{Filling out the matrix equation}
  \begin{enumerate}[<+-| alert@+>]
  \item Populate the unknowns vector with the list of unknown variables.
  \item Populate the right-hand side vector with the right-hand sides
    of the equations.
  \item Populate each row of the coefficient matrix with coefficients
    from the left-hand side of the equations.
  \end{enumerate}
  \begin{displaymath}
    \left[ \begin{array}{rrrrrr}
        \onslide<3-> 1 & 1 & -1 & -1 & 0 & -1 \\
        \onslide<4-> 0 & -9 & 1 & 4 & 0 & 7 \\
        \onslide<5-> 0 & 0 & 1 & 1 & -1 & 0 \\
        \onslide<6-> 0 & 0 & 0 & -3 & 2 & 0 \\
        \onslide<7-> 0 & 0 & 0 & 0 & 1 & 1 \\
        \onslide<8-> 0 & 0 & 0 & 0 & 0 & -4 \\
      \end{array} \onslide<1-> \right]
    \onslide<1-> \left\{ \begin{array}{c}
        T_A \onslide<1-> \\
        T_B \onslide<1-> \\
        T_C \onslide<1-> \\
        T_D \onslide<1-> \\
        T_E \onslide<1-> \\
        T_F \onslide<1-> \\
      \end{array} \right\} =
    \onslide<1-> \left\{ \begin{array}{r}
        \onslide<2-> P_1 \\
        -5P_1\onslide<2->  \\
        P_2 \onslide<2-> \\
        -P_2 \onslide<2-> \\
        P_3 \onslide<2-> \\
        -P_3 \onslide<2-> \\
      \end{array} \onslide<1-> \right\}
  \end{displaymath}
}