Answer
$x=3, y=2 \text{ or } (3,2)$
Work Step by Step
We will write the system $\left\{\begin{array}{r}{2 x+y=8}\\{x+y=5}\end{array}\right.$ in matrix form as: $AX=B$
where, $X=\left[\begin{array}{l}x\\y \end{array}\right]$
We have: $A=\left[\begin{array}{ll}{2}&{1}\\{1}&{1}\end{array}\right]$, and its inverse is: $A^{-1}=\left[\begin{array}{rr}{1}&{-1}\\{-1}&{2}\end{array}\right]$
Thus, the solution of the given matrix can be expressed as:
$X=A^{-1}B=\left[\begin{array}{rr}
{1}&{-1}\\{-1}&{2}\end{array}\right]\left[\begin{array}{l}
8\\5\end{array}\right]$
$\left[\begin{array}{l}
x\\y \end{array}\right]=\left[\begin{array}{l} 8-5\\
-8+10 \end{array}\right]=\left[\begin{array}{l}
3\\2\end{array}\right]$
So, our solution is: $(x, y)=(3,2)$
