[Tex/LaTex] How to write the solving steps of a system of equations

Question

I'm trying to do the following in LaTeX:

The box at the end doesn't have to be there. I've tried using cases, from the amsmath package, but it doesn't align correctly with the equations on top, nor is the formatting very pretty:

This is the code I used:

\begin{align*}
    \sum \vec{F} &= ma \\
    \vec{R_n} + \vec{Fg} + \vec{F_a} &= ma \\

    \begin{cases}
        \vec{F_a} &= ma_c\\
        \vec{R_n} - \vec{F_g} &= 0
    \end{cases}  

    \begin{cases}
        uR_n &= m\frac{v^2}{r}\\
        R_n &= mg
    \end{cases}  

    \begin{cases}
        ug &= \frac{v^2}{r}\\
        R_n &= mg
    \end{cases}  

    \begin{cases}
        \sqrt{ugr} &= v\\
    \end{cases}
\end{align*}

Thanks in advance, I'm a LaTeX beginner 🙂

Answer 1

Some improvements with mathtools and esvect (for nicer-looking arrow tips), and a slightly different layout:

\documentclass{article}
\usepackage{mathtools, esvect}

\begin{document}


\begin{align*}
                  & \mkern1.5mu \sum \vv{F} = ma \Leftrightarrow\vv*{R}{n} + \vv*{F}{g} + \vv*{F}{a} = ma \\
  \Leftrightarrow & \begin{dcases}
  \vv{F_a} = ma_c\\
  \vv*{R}{n} - \vv*{F}{g} = 0
  \end{dcases}
  %
  \Leftrightarrow \begin{dcases}
  uR_n = m\frac{v^2}{r}\\
  R_n = mg
  \end{dcases}
  %
  \Leftrightarrow \begin{dcases}
  ug = \frac{v^2}{r}\\
  R_n = mg
  \end{dcases}\\
  \Leftrightarrow & \hspace*{\fboxsep} \boxed{\sqrt{ugr} = v}
\end{align*}

\end{document}