System of equations

Question

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}
\begin{equation}
\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{equation}
 \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

Answer 1

A solution using the cases environment:

\documentclass[]{article}

\usepackage{amsmath}

\begin{document}
\begin{equation}
    \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{equation}
\end{document}

Answer 2

A solution using array (no packages needed):

\documentclass[]{article}

\begin{document}
\begin{equation}
  \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{equation}
\end{document}

Answer 3

\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}

Answer 4

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}
\usepackage{empheq} %% loads mathtools, which loads amsmath
\DeclarePairedDelimiter{\abs}\lvert\rvert

\begin{document}

\begin{spreadlines}{1ex}
\begin{equation}
\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}
\end{equation}
\end{spreadlines}

\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} 

Answer 5

For those like me that came here just to know how to represent a system with two lines of equations and don't care about the rest:

---

\[
A =
\left\{ 
    \begin{array}{l}
        a &\\
        b
    \end{array} 
\right.
\]

(screenshot taken from Obsidian markdown editor)

---

Simple explanation

• You put your equations inside \begin{array}{l} \end{array}, the l mean align left.
• You separate every element of the array with & and use \\ to change line and put them on different lines.
• \left\{ creates the curly brace on the left and \right. means there's no visible delimiter on the right.
• You can add as many lines as you want, likes this:

\[
A =
\left\{ 
    \begin{array}{l}
        a &\\
        b &\\
        c &\\
        d
    \end{array} 
\right.
\]

Answer 6

A solution with a customized environment in mathematical expression or equation in the preamble

\newenvironment{system}%
{\left\lbrace\begin{array}{@{}l@{}}}%
{\end{array}\right.}

And in the text for example

\begin{equation}
\begin{system}
equation 1  \\
equation 2 
\end{system}
\end{equation}

This code works but was suggested to me by a friend during I was writing my master's thesis

Answer 7

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}

Answer 8

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}