Question

Examine the consistency of the system of equations.
2x-y=5,
x+y=4

Answer 1

The given system of equations is:
2x − y = 5
x + y = 4
The given system of equations can be written in the form of AX = B, where

A=$\begin{bmatrix}2&-1\\\1&1\end{bmatrix}$, X=$\begin{bmatrix}x\\\y\end{bmatrix}$and B=$\begin{bmatrix}5\\\4\end{bmatrix}$.

Now IAI=2(1)-(-1)=2+1=3≠0
∴ A is non-singular.
Therefore, A-1 exists.

Hence, the given system of equations is consistent