1.
begin{eqnarray} Ly = lambda y end{eqnarray}
2.
begin{gather*} begin{split} b=1\ a=b end{split}\[6pt] end{gather*}
3.
begin{gather*} begin{split} a &= m\ &= k end{split}\[6pt] begin{align} b &= i ,\ c &= j end{align} end{gather*}