Solve this

Given: $3 x+y=5$

$-6 x-2 y=9$

$D=\left|\begin{array}{cr}3 & 1 \\ -6 & -2\end{array}\right|=-6+6=0$

$D_{1=}\left|\begin{array}{rr}5 & 1 \\ 9 & -2\end{array}\right|=-10-9=-19$

$D_{2}=\left|\begin{array}{cc}3 & 5 \\ -6 & 9\end{array}\right|=27+30=57$

Here, $D_{1}$ and $D_{2}$ are non-zero, but $D$ is zero. Thus, the system of linear equations is inconsistent.