$$5x+3y=- \frac { } { }$$
$x=\frac{-3y-1}{5}$
$$5x+3y=-1$$
$$5x=-1-3y$$
$$5x=-3y-1$$
$$\frac{5x}{5}=\frac{-3y-1}{5}$$
$$x=\frac{-3y-1}{5}$$
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$y=\frac{-5x-1}{3}$
$$3y=-1-5x$$
$$3y=-5x-1$$
$$\frac{3y}{3}=\frac{-5x-1}{3}$$
$$y=\frac{-5x-1}{3}$$