Answer
$x=-7, y=-28 \text{ or } (-7,-28)$
Work Step by Step
We will write the system $\left\{\begin{array}{r}{-4x+y=0}\\{6x-2y=14}\end{array}\right.$ 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:
$X=A^{-1}B=\left[\begin{array}{rr}{-1}&{-1/2}\\{-3}&{-2}\end{array}\right]\left[\begin{array}{l}
0\\14\end{array}\right]$
$\left[\begin{array}{l}
x\\y \end{array}\right]=\left[\begin{array}{l} 0-7\\
0-28 \end{array}\right]=\left[\begin{array}{l}
-7\\-28\end{array}\right]$
So, our solution is:: $(x, y)=(-7,-28)$