In a system of $3$ linear non-homogeneous equation with three unknowns,if $\bigtriangleup=0\;$ and $\;\bigtriangleup_{x}=0 ,\bigtriangleup_y\neq 0 $ and $ \bigtriangleup_z=0$ then the system has

Question

\[\](1) unique solution$\;$ (2)two solutions\[\](3) infinitely many solutions $\;$(4) no solutions