$$3x-5y=3$$
$x=\frac{5y}{3}+1$
$$3x=3+5y$$
$$3x=5y+3$$
$$\frac{3x}{3}=\frac{5y+3}{3}$$
$$x=\frac{5y+3}{3}$$
$$x=\frac{5y}{3}+1$$
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$y=\frac{3\left(x-1\right)}{5}$
$$-5y=3-3x$$
$$\frac{-5y}{-5}=\frac{3-3x}{-5}$$
$$y=\frac{3-3x}{-5}$$
$$y=\frac{3x-3}{5}$$
