$2x - y = 5,x + y = 4.$

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

where
$A = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}2&{ - 1}\\1&1\end{array}} \right],X = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}x\\y\end{array}} \right],B = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}5\\4\end{array}} \right]$

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

Hence, system of equations is consistent.