\documentclass{article}
\usepackage{amsmath,empheq}


\begin{document}


\begin{empheq}{alignat=2}
&(H-\lambda I)x=x^{(k)}=kx^{(k-1)}+ p^{(k)}(\lambda)e_1 ,& \qquad k=0,1,2,\ldots \label{eq35}  \\
&    y^{(k)}(H-\lambda I)=ky^{(k-1)H}+ p^{(k)}(\lambda)e_n^T, &  k=0,1,2,\ldots \label{eq36}
\end{empheq}

\begin{empheq}[box=\fbox]{align}
&(H-\lambda I)x=x^{(k)}=kx^{(k-1)}+ p^{(k)}(\lambda)e_1 ,& \qquad k=0,1,2,\ldots \label{eq35}  \\
&    y^{(k)}(H-\lambda I)=ky^{(k-1)H}+ p^{(k)}(\lambda)e_n^T, &  k=0,1,2,\ldots \label{eq36}
\end{empheq}


\begin{align}
&(H-\lambda I)x=x^{(k)}=kx^{(k-1)}+ p^{(k)}(\lambda)e_1 ,& \qquad k=0,1,2,\ldots \label{eq35}  \\
&    y^{(k)}(H-\lambda I)=ky^{(k-1)H}+ p^{(k)}(\lambda)e_n^T, &  k=0,1,2,\ldots \label{eq36}
\end{align}
\end{document}