Answer
$x=\dfrac{-1}{2}, y=-3 \text{ or } \left(\dfrac{-1}{2},3\right)$
Work Step by Step
We will write the system $\left\{\begin{array}{r}{-4x+y=5}\\{6x-2y=-9}\end{array}\right.$ in matrix form as: $AX=B$
where, $X=\left[\begin{array}{l}x\\y \end{array}\right]$
We have: $A=\left[\begin{array}{ll}{-4}&{1}\\{6}&{-2}\end{array}\right]$, and its inverse is: $A^{-1}=\left[\begin{array}{rr}{-1}&{-1/2}\\{-3}&{-2}\end{array}\right]$
Thus, the solution of the given matrix can be expressed as:
$X=A^{-1}B=\left[\begin{array}{rr}{-1}&{-1/2}\\{-3}&{-2}\end{array}\right]\left[\begin{array}{l}
5\\-9\end{array}\right]$
$\left[\begin{array}{l}
x\\y \end{array}\right]=\left[\begin{array}{l} -5+\dfrac{9}{2}\\
-15+18 \end{array}\right]=\left[\begin{array}{l}
\dfrac{-1}{2}\\3\end{array}\right]$
So, our solution is:: $(x, y)=\left(\dfrac{-1}{2},3\right)$
