$x + 3y = 5,2x + 6y = 8.$

The system of equations can be written in the form $AX = B$,

where
$A = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&3\\2&6\end{array}} \right],X = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}x\\y\end{array}} \right],B = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}5\\8\end{array}} \right]$

Now, $|A| = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&3\\2&6\end{array}} \right| = 6 - 6 = 0$

Hence, A is singular matrix. So, we calculate (adj A) B.
$adj\;A = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}6&{ - 3}\\{ - 2}&1\end{array}} \right]$

Now, (adj A)B $= \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}6&{ - 3}\\{ - 2}&1\end{array}} \right]\left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}5\\8\end{array}} \right]$

$= \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}{30 - 24}\\{ - 10 + 8}\end{array}} \right] = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}6\\{ - 2}\end{array}} \right] \ne \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}0\\0\end{array}} \right]$

Hence, equations are inconsistent with no solution.