Question

Examine the consistency of the system of equations

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

Answer 1

The given system can be written as AX=B, where
$A=\left[\begin{array}{cc}2& -1\\ 1& 1\end{array}\right],X=\left[\begin{array}{c}x\\ y\end{array}\right]andB=\left[\begin{array}{c}5\\ 4\end{array}\right]|A|=\left[\begin{array}{cc}2& -1\\ 1& 1\end{array}\right]=2\left(1\right)-\left(1\right)1=2+1=3\ne 0$
$\therefore$ A is non-singular. Therefore, $A^{-1}$ exists.
Hence, the given system of equations is consistent.