$x + 2y = 2,2x + 3y = 3.$

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

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

Now, $|A| = 3 - 4 = - 1 \ne 0$

Hence, system of equations is consistent.