#### Answer

$x=-2$ and $y=-7$

#### Work Step by Step

Given the equations $-6x+y=5$ and $4x-2y=6$
$1.)$ Isolate $y$ in the first equation: $-6x+y=5\longrightarrow y=6x+5$
$2.)$ Substitute $y$ in the second equation: $4x-2y=6\longrightarrow 4x-2(6x+5)=6$
$3.)$ Divide by $2$: $4x-2(6x+5)=6\longrightarrow 2x-(6x+5)=3$
$4.)$ Solve for $x$: $2x-(6x+5)=3\longrightarrow 2x-6x-5=3\longrightarrow -4x=3+5\longrightarrow x=\dfrac{8}{-4}=-2$
$5.)$ Substitute $x$ in the equation from step $1$: $y=6x+5\longrightarrow y=6(-2)+5\longrightarrow y=-12+5\longrightarrow y=-7$
Therefore the solutions is $x=-2$ and $y=-7$