$$5x+7y=-1$$
$x=\frac{-7y-1}{5}$
$$5x=-1-7y$$
$$5x=-7y-1$$
$$\frac{5x}{5}=\frac{-7y-1}{5}$$
$$x=\frac{-7y-1}{5}$$
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$y=\frac{-5x-1}{7}$
$$7y=-1-5x$$
$$7y=-5x-1$$
$$\frac{7y}{7}=\frac{-5x-1}{7}$$
$$y=\frac{-5x-1}{7}$$
