# How to align two systems of equations side by side?

I have the following systems of equations and I want them to be side by side, each of them having a brief description below, which is the text I've written after the \end{cases}\\?

Below is my source code, which outputs the two systems, but the one on the right is a bit lower than the other one:

\begin{flushleft}
\begin{cases}
I_{50}+I_{10}=I_{03}\\
I_{21}=I_{12}+I_{10}\\
I_{12}+I_{32}=I_{21}\\
I_{03}=I_{32}+I_{34}\\
I_{34}=I_{451}+I_{452}\\
\end{cases}\\, pentru legea I, si
\end{flushleft}
\begin{flushright}
\begin{cases}
U_{30}+U_{01}+U_{121}+U_{23}=0\\
U_{34}+U_{452}+U_{50}+U_{30}=0\\
U_{121}+U_{122}=0\\
U_{451}+U_{452}=0\\
\end{cases} \\
pentru legea a II-a
\end{flushright}


Two solutions, one with the flalign* environment, the other with alignat* lets you control the ditance between the two systems:

    \documentclass{article}
\usepackage[showframe]{geometry}
\usepackage{mathtools}

\begin{document}
A solution with \texttt{flalign*}:
\begin{flalign*}
& \begin{aligned} & \begin{cases}
I_{50}+I_{10}=I_{03}\\
I_{21}=I_{12}+I_{10}\\
I_{12}+I_{32}=I_{21}\\
I_{03}=I_{32}+I_{34}\\
I_{34}=I_{451}+I_{452}\\
\end{cases}\\
\MoveEqLeft[-1]\text{pentru legea I, si}
\end{aligned}
& &
\begin{aligned}
& \begin{cases}
U_{30}+U_{01}+U_{121}+U_{23}=0\\
U_{34}+U_{452}+U_{50}+U_{30}=0\\
U_{121}+U_{122}=0\\
U_{451}+U_{452}=0\\
\end{cases} \\
\MoveEqLeft[-1]\text{si pentru legea a II-a}
\end{aligned}
\end{flalign*}
\vskip 3ex
A solution with \texttt{alignat*}:
\begin{alignat*}{2}
& \begin{aligned} & \begin{cases}
I_{50}+I_{10}=I_{03}\\
I_{21}=I_{12}+I_{10}\\
I_{12}+I_{32}=I_{21}\\
I_{03}=I_{32}+I_{34}\\
I_{34}=I_{451}+I_{452}\\
\end{cases}\\
\MoveEqLeft[-1]\text{pentru legea I, si}
\end{aligned}
& \hskip 6em &
\begin{aligned}
& \begin{cases}
U_{30}+U_{01}+U_{121}+U_{23}=0\\
U_{34}+U_{452}+U_{50}+U_{30}=0\\
U_{121}+U_{122}=0\\
U_{451}+U_{452}=0\\
\end{cases} \\[3.3ex]
\MoveEqLeft[-1]\text{si pentru legea a II-a}
\end{aligned}
\end{alignat*}

\end{document}


With align* in a tabularx:

% arara: pdflatex

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[romanian]{babel}
\usepackage{combelow}
\usepackage{newunicodechar}
\newunicodechar{ș}{\cb{s}}
\usepackage{mathtools}
\usepackage{tabularx}
\usepackage{blindtext}

\begin{document}
\blindtext
\begin{tabularx}{\textwidth}{XX}
{\begin{align*}
&\begin{cases}
I_{50}+I_{10}=I_{03}\\
I_{21}=I_{12}+I_{10}\\
I_{12}+I_{32}=I_{21}\\
I_{03}=I_{32}+I_{34}\\
I_{34}=I_{451}+I_{452}\\
\end{cases}\\
&\text{, pentru legea I, și}\end{align*}}
&
{\begin{align*}
&\begin{cases}
U_{30}+U_{01}+U_{121}+U_{23}=0\\
U_{34}+U_{452}+U_{50}+U_{30}=0\\
U_{121}+U_{122}=0\\
U_{451}+U_{452}=0\\
\end{cases}\\
\\ % optional
&\text{pentru legea a II-a}\end{align*}}
\end{tabularx}
\blindtext
\end{document}


with align* and aligned

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[romanian]{babel}
\usepackage{combelow}
\usepackage{newunicodechar}
\newunicodechar{ș}{\cb{s}}
\usepackage{mathtools}
\usepackage{blindtext}

\begin{document}
\blindtext

\begin{align*}
&\left\{
\begin{aligned}
I_{50}+I_{10}=I_{03}\\
I_{21}=I_{12}+I_{10}\\
I_{12}+I_{32}=I_{21}\\
I_{03}=I_{32}+I_{34}\\
I_{34}=I_{451}+I_{452}\\
\end{aligned}\right.
&
\left\{\begin{aligned}
U_{30}+U_{01}+U_{121}+U_{23}=0\\
U_{34}+U_{452}+U_{50}+U_{30}=0\\
U_{121}+U_{122}=0\\
U_{451}+U_{452}=0\\
\end{aligned}\right. \\
&\text{, pentru legea I, și}
&\text{pentru legea a II-a}
\end{align*}

\blindtext
\end{document}