#### Answer

$x=2, y=-1 \text{ or } (2,-1)$

#### Work Step by Step

We will write the system $\left\{\begin{array}{r}{6x+5y=7}\\{2x+2y=2}\end{array}\right.$ in matrix form as: $AX=B$
where, $X=\left[\begin{array}{l}x\\y \end{array}\right]$
We have: $A=\left[\begin{array}{ll}{6}&{5}\\{2}&{2}\end{array}\right]$, and its inverse is: $A^{-1}=\left[\begin{array}{rr}{1}&{-5/2}\\{-1}&{3}\end{array}\right]$
Thus, the solution of the given matrix can be expressed as:
$X=A^{-1}B=\left[\begin{array}{rr}{1}&{-5/2}\\{-1}&{3}\end{array}\right]\left[\begin{array}{l}
7\\2\end{array}\right]$
$\left[\begin{array}{l}
x\\y \end{array}\right]=\left[\begin{array}{l} 7-5\\
-7+6 \end{array}\right]=\left[\begin{array}{l}
2\\-1\end{array}\right]$
So, our solution is:(2,-1)$