\documentclass{article}
\usepackage{tikz}
\usepackage{mathtools}
\usepackage{euler}
\everymath{\displaystyle}
\begin{document}
$\begin{cases}
x'&=\frac{\Delta D_{x'}}{D} =\frac{\begin{vmatrix}
1&-y\\ 0&x
\end{vmatrix}}{x^2+y^2}\\
y'&=\frac{\Delta D_{y'}}{D} =\frac{\begin{vmatrix}
x&1\\ x&0
\end{vmatrix}}{x^2+y^2}
\end{cases} \\
\begin{matrix}
x'&=\frac{\Delta D_{x'}}{D} =\frac{\begin{vmatrix}
1&-y\\ 0&x
\end{vmatrix}}{x^2+y^2}=\frac{x}{ x^2+y^2}\\
\tikz{\node[overlay] at (-.2,.7) {$\left\{\rule{0pt}{.95cm}\right.$};}
y'&=\frac{\Delta D_{y'}}{D} =\frac{\begin{vmatrix}
x&1\\ x&0
\end{vmatrix}}{x^2+y^2}=\frac{-y}{ x^2+y^2}
\end{matrix}$
\end{document}
\usepackage{tikz}
\usepackage{mathtools}
\usepackage{euler}
\everymath{\displaystyle}
\begin{document}
$\begin{cases}
x'&=\frac{\Delta D_{x'}}{D} =\frac{\begin{vmatrix}
1&-y\\ 0&x
\end{vmatrix}}{x^2+y^2}\\
y'&=\frac{\Delta D_{y'}}{D} =\frac{\begin{vmatrix}
x&1\\ x&0
\end{vmatrix}}{x^2+y^2}
\end{cases} \\
\begin{matrix}
x'&=\frac{\Delta D_{x'}}{D} =\frac{\begin{vmatrix}
1&-y\\ 0&x
\end{vmatrix}}{x^2+y^2}=\frac{x}{ x^2+y^2}\\
\tikz{\node[overlay] at (-.2,.7) {$\left\{\rule{0pt}{.95cm}\right.$};}
y'&=\frac{\Delta D_{y'}}{D} =\frac{\begin{vmatrix}
x&1\\ x&0
\end{vmatrix}}{x^2+y^2}=\frac{-y}{ x^2+y^2}
\end{matrix}$
\end{document}