Question

Examine the consistency of the system of equations

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

Answer 1

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