$$5x+3y=-9$$
$x=\frac{-3y-9}{5}$
$$5x=-9-3y$$
$$5x=-3y-9$$
$$\frac{5x}{5}=\frac{-3y-9}{5}$$
$$x=\frac{-3y-9}{5}$$
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$y=-\frac{5x}{3}-3$
$$3y=-9-5x$$
$$3y=-5x-9$$
$$\frac{3y}{3}=\frac{-5x-9}{3}$$
$$y=\frac{-5x-9}{3}$$
$$y=-\frac{5x}{3}-3$$