\documentclass[12pt,a4paper]{article}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{empheq}



\begin{document}


\begin{empheq}[       left={\empheqlbrace}]{align}
 y_m&=x_m - \frac{f(x_m)}{f'(x_m)},\\
z_m&=y_m - G\left( \frac{f(y_m)}{f(x_m)}\right)  \frac{f(y_m)}{f'(x_m)},\\
x_{m+1}&=z_m - \frac{\mu}{\lambda + \nu q_m^2}\frac{f(z_m)}{ K - C(y_m -z_m) - D(y_m - z_m)^2}
\end{empheq}
 \setlength{\jot}{20pt}
\begin{empheq}[       left={\empheqlbrace}]{align}
 y_m&=x_m - \frac{f(x_m)}{f'(x_m)},\\
z_m&=y_m - G\left( \frac{f(y_m)}{f(x_m)}\right)  \frac{f(y_m)}{f'(x_m)},\\
x_{m+1}&=z_m - \frac{\mu}{\lambda + \nu q_m^2}\frac{f(z_m)}{ K - C(y_m -z_m) - D(y_m - z_m)^2}
\end{empheq}
\end{document}