The system of linear equations, $\mathrm{x}+\mathrm{y}+\mathrm{z}=6,$$\mathrm{x}+2\mathrm{y}+3\mathrm{z}=14$$\mathrm{and} 2\mathrm{x}+5\mathrm{y}+\mathrm{\lambda z}=\mathrm{\mu }$ have 

$\begin{array}{l}\mathrm{x}+\mathrm{y}+\mathrm{z}=6\\ \mathrm{x}+2\mathrm{y}+3\mathrm{z}=14;2\mathrm{x}+5\mathrm{y}+\mathrm{\lambda z}=\mathrm{\mu }\end{array}$
$\mathrm{D}=\left|\begin{array}{l}1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\\ 1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}3\\ 2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}5\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{\lambda }\end{array}\right|,{\mathrm{D}}_{\mathrm{x}}=\left|\begin{array}{ccc}6& 1& 1\\ 14& 2& 3\\ \mathrm{\mu }& 5& \mathrm{\lambda }\end{array}\right|$
${\mathrm{D}}_{\mathrm{y}}=\left|\begin{array}{ccc}1& 6& 1\\ 1& 14& 3\\ 2& \mathrm{\mu }& \mathrm{\lambda }\end{array}\right|,{\mathrm{D}}_{\mathrm{z}}=\left|\begin{array}{ccc}1& 1& 6\\ 1& 2& 14\\ 2& 5& \mathrm{\mu }\end{array}\right|$
For unique solution $\mathrm{D}\ne 0\Rightarrow \mathrm{\lambda }-8\ne 0$  for D non zero.
For infinitely many solutions $\mathrm{D}={\mathrm{D}}_{\mathrm{x}}={\mathrm{D}}_{\mathrm{y}}={\mathrm{D}}_{\mathrm{z}}=0$

$D_z=\mu -36$
Solve for value of $\mathrm{\lambda }\text{ and }\mathrm{\mu }$.