$$4x+2y=-6$$
$x=\frac{-y-3}{2}$
$$4x=-6-2y$$
$$4x=-2y-6$$
$$\frac{4x}{4}=\frac{-2y-6}{4}$$
$$x=\frac{-2y-6}{4}$$
$$x=\frac{-y-3}{2}$$
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$y=-2x-3$
$$2y=-6-4x$$
$$2y=-4x-6$$
$$\frac{2y}{2}=\frac{-4x-6}{2}$$
$$y=\frac{-4x-6}{2}$$
$$y=-2x-3$$
