# System of equations

I am a beginner in Latex and I would like to know how I can write this system of equations

But I don't know how.

I have tried this code:

\documentclass{article}
\usepackage{mathtools}
\usepackage{nccmath}
$$\centering \left\{\begin{split} \mfrac{k_{i\omega}}{k_{p\omega}} &=2\pi \times 10 \\ |\mfrac{(k_{p\omega}s + k_{i\omega})}{s}.\mfrac{1}{(T s + 1)}| &= 1 \\ \end{split}\right.$$
\end{document}


But I couldn't get the absolute value symbol as shown in the figure above and also I couldn't display the s=jw under the absolute value symbol and also the equations aren't aligned

A solution using the cases environment:

\documentclass[]{article}

\usepackage{amsmath}

\begin{document}
$$\begin{cases} k_{i\omega}/k_{p\omega}=2\pi\times 10\\ \left\lvert\frac{k_{p\omega}s+k_{i\omega}}{s}\cdot\frac{1}{Ts+1}\right\rvert_{S=\mathrm{j}\cdot2\pi}=1 \end{cases}\,.$$
\end{document}


• Personally, I do not prefer using cases if there are no cases semantically speaking (WYSIWYM). – ivankokan Dec 12 '19 at 23:01
• @ivankokan that's why I've added the cleaner array approach. – Skillmon likes topanswers.xyz Dec 12 '19 at 23:02

A solution using array (no packages needed):

\documentclass[]{article}

\begin{document}
$$\left\{\begin{array}{@{}l@{}} k_{i\omega}/k_{p\omega}=2\pi\times 10\\ \left| \frac{k_{p\omega}s+k_{i\omega}}{s}\cdot\frac{1}{Ts+1} \right|_{S=\mathrm{j}\cdot2\pi}=1 \end{array}\right.\,.$$
\end{document}


Here is a way to do it, with the dcases and spreadlines environments, from mathtools. The latter package lets you define additional vertical spacing between rows of a multiline equation, which is necessary here, due to the fractions in each line.

I added another solution with the empheq package.

Unrelated: preferably load nccmath before mathtools, as there might be problems with the \intertext command. Also, I defined an \abs command for the absolute value with the \DeclarePairedDelimiter command from mathtools to have the vertical lines adjusted to their contents.

\documentclass{article}
\usepackage{nccmath}
\DeclarePairedDelimiter{\abs}\lvert\rvert

\begin{document}

$$\begin{dcases} \mfrac{k_{i\omega}}{k_{p\omega}} =2\pi \times 10 \\ \abs*{\mfrac{(k_{p\omega}s + k_{i\omega})}{s}\cdot \mfrac{1}{(T s + 1)}}= 1 \end{dcases}$$

\begin{empheq}[left=\empheqlbrace]{equation}
\begin{aligned}
& \mfrac{k_{i\omega}}{k_{p\omega}} =2\pi \times 10 \\
& \abs*{\mfrac{(k_{p\omega}s + k_{i\omega})}{s}\cdot \mfrac{1}{(T s + 1)}}= 1
\end{aligned}
\end{empheq}

\end{document}


• What is the purpose of \abs*{stuff} compared with \abs{stuff}? – pzorba75 Dec 13 '19 at 4:51
• It adds a pair of implicit \left ... \right. Another solution would be, say, \abs[\bigg]{stuff}, which adds a pair of implicit \biggl ... \biggr. – Bernard Dec 13 '19 at 8:12
\documentclass{article}

\usepackage{amsmath}

\begin{document}
\begin{equation*}
\left\{
\begin{aligned}
& k_{i\omega} / k_{p\omega} = 2\pi \times 10 \\
& {\left|
\frac{k_{p\omega}s + k_{i\omega}}{s} \cdot \frac{1}{Ts + 1}
\right|}_{s = j \cdot 2\pi} = 1
\end{aligned}
\right.
\end{equation*}
\end{document}


• In fact, I want the equations to aligned on the left not based on the equal operator? – littleesuf Dec 12 '19 at 22:56
• I want the first equation to be on the left too – littleesuf Dec 12 '19 at 22:59
• Edited. In general, use the & to specify the place of alignment. – ivankokan Dec 12 '19 at 23:13

I added my humble proposal using an array for my MWE. The output is very similar to the previous answers. The screenshot is:

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\begin{document}
$\left\{ \begin{array}{ll} k_{i\omega}/k_{p\omega}=2\pi\times 10 &\\ \Bigl|\frac{k_{p\omega}s + k_{i\omega}}{s}\cdot\frac{1}{Ts+1} \Bigr|_{S=\mathrm{j}\cdot 2\pi}=1 \end{array} \right.$
\end{document}


For fun:

This uses the amsmath package due to the use of \substack. This avoids any align, aligned, gather, array, ... environments but I had to pay the price of aligning manually.

\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
$$\Large\left\{\substack{\hspace{-2.1cm}\,k_{i\omega}/k_{p\omega}\,=\,2\pi\,\times\, 10\vspace{0.2cm}\\\,\left|\frac{k_{p\omega}s\,+\,k_{i\omega}}{s}\,\cdot\,\frac{1}{Ts\,+\,1}\right|_{s\,=\,{\rm j}\,\cdot\,2\pi}\,=\,1}\right.$$
\end{document}