Latex: fail to show line breaks in formula with ```\\``` - latex

Question

I'm using rmarkdown to knit to pdf. However, line break \\ doesn't take effect. I suspect something is wrong with my package amsmath, because running the tex file also shows the same problem. But I don't know how to fix it.
(I installed R and Rstudio with tinytex, then installed tex live 2021. I don't know whether this can be the cause.)
The code is shown below:
---
title: "test"
date: '2022-04-07'
output:
word_document: default
pdf_document:
keep_tex: yes
---
$$
a = b \\
c = d
$$
Also, when I try knit to word, there are warning messages
[WARNING] Could not convert TeX math
a = b \
c = d
, rendering as TeX:
a = b \
^
unexpected control sequence \
expecting "%", "\label", "\tag", "\nonumber" or whitespace
Building the tex file, I still cannot see the expected linebreak in the output pdf. The tex file is shown below.
% Options for packages loaded elsewhere
\PassOptionsToPackage{unicode}{hyperref}
\PassOptionsToPackage{hyphens}{url}
%
\documentclass[
]{article}
\usepackage{amsmath,amssymb}
\usepackage{lmodern}
\usepackage{iftex}
\ifPDFTeX
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{textcomp} % provide euro and other symbols
\else % if luatex or xetex
\usepackage{unicode-math}
\defaultfontfeatures{Scale=MatchLowercase}
\defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1}
\fi
% Use upquote if available, for straight quotes in verbatim environments
\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
\IfFileExists{microtype.sty}{% use microtype if available
\usepackage[]{microtype}
\UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
}{}
\makeatletter
\#ifundefined{KOMAClassName}{% if non-KOMA class
\IfFileExists{parskip.sty}{%
\usepackage{parskip}
}{% else
\setlength{\parindent}{0pt}
\setlength{\parskip}{6pt plus 2pt minus 1pt}}
}{% if KOMA class
\KOMAoptions{parskip=half}}
\makeatother
\usepackage{xcolor}
\IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available
\IfFileExists{bookmark.sty}{\usepackage{bookmark}}{\usepackage{hyperref}}
\hypersetup{
pdftitle={test},
hidelinks,
pdfcreator={LaTeX via pandoc}}
\urlstyle{same} % disable monospaced font for URLs
\usepackage[margin=1in]{geometry}
\usepackage{graphicx}
\makeatletter
\def\maxwidth{\ifdim\Gin#nat#width>\linewidth\linewidth\else\Gin#nat#width\fi}
\def\maxheight{\ifdim\Gin#nat#height>\textheight\textheight\else\Gin#nat#height\fi}
\makeatother
% Scale images if necessary, so that they will not overflow the page
% margins by default, and it is still possible to overwrite the defaults
% using explicit options in \includegraphics[width, height, ...]{}
\setkeys{Gin}{width=\maxwidth,height=\maxheight,keepaspectratio}
% Set default figure placement to htbp
\makeatletter
\def\fps#figure{htbp}
\makeatother
\setlength{\emergencystretch}{3em} % prevent overfull lines
\providecommand{\tightlist}{%
\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\setcounter{secnumdepth}{-\maxdimen} % remove section numbering
\ifLuaTeX
\usepackage{selnolig} % disable illegal ligatures
\fi
\title{test}
\author{}
\date{\vspace{-2.5em}2022-04-07}
\begin{document}
\maketitle
\[
a = b \\
c = d
\]
\end{document}

Answer 1

I think this should perfectly answer your question:
https://tex.stackexchange.com/questions/46189/how-do-i-add-a-line-break-in-display-math-mode
In short: \[ \] is made for one equation/one line of math. To add a line-break, you should use an environment like gather or align. The code for align would look like this in your tex-code:
\begin{align}
a &= b \\
c &= d
\end{align}
If you don't need numbering of your equations, you would use the starred version of the respective environment (gather*, align*. Like this:
\begin{align*}
a &= b \\
c &= d
\end{align*}
If the link I provided does not fit your problem, please explain why. I am happy to correct this answer.