Question

Examine the consistency of the system of equations

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

Answer 1

Given system of equations

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

This can be written as

$AX=B$

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

Here, $|A|=2-(-1)=3$

Since, $|A|\ne 0$

Hence, $A^{-1}$ exists and the system has a unique solution.