# How to make one case equation point to another case equation?

I want to display the following

I'm trying to realize it with the following code

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}

\begin{document}
$$\begin{cases} &a + b\\ & b + c \end{cases} \implies \begin{cases} & c + d\\ & d + e \end{cases}$$
\end{document}


But this gives me a lot of errors and the wrong output

Does anyone know how to fix this?

• Remove the blank line within the equation. Or, if you want it for aesthetic/coding reasons, insert a %. – Werner Oct 21 '20 at 4:17
• – Werner Oct 21 '20 at 4:18

In addition to getting rid of the blank line between the two cases environments, you should also (a) get rid of the & alignment operators (since you're not really making use of much of the cases machinery) and (b) insert a \quad directive after \implies in order to even out the spacing to the left and right of the \implies (aka \Longrightarrow) symbol.
\documentclass{article}
$$\begin{cases} a + b\\ b + c \end{cases} \implies \quad \begin{cases} c + d\\ d + e \end{cases}$$