\documentclass[12pt]{article}
\usepackage{mathtools}
\begin{document}
\begin{equation*}
\left.\begin{array}{ll}
y'_{1} &= a_{11}y_{1}+a_{12}y_{2}+\cdots+a_{1n}y_{n}, \\
y'_{2} &= a_{21}y_{1}+a_{22}y_{2}+\cdots+a_{2n}y_{n}, \\
\hdotsfor{2}\\
y'_{n} &= a_{n1}y_{1}+a_{n2}y_{2}+\cdots+a_{nn}y_{n}
\end{array} \right\}
\quad
\end{equation*}
\end{document}