$$\frac{5-x}{3}-\frac{3-2y}{7}=1$$
$x=\frac{6y+5}{7}$
$$7\left(5-x\right)-3\left(3-2y\right)=21$$
$$35-7x-3\left(3-2y\right)=21$$
$$35-7x-9+6y=21$$
$$26-7x+6y=21$$
$$-7x+6y=21-26$$
$$-7x+6y=-5$$
$$-7x=-5-6y$$
$$-7x=-6y-5$$
$$\frac{-7x}{-7}=\frac{-6y-5}{-7}$$
$$x=\frac{-6y-5}{-7}$$
$$x=\frac{6y+5}{7}$$
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$y=\frac{7x-5}{6}$
$$6y=-5+7x$$
$$6y=7x-5$$
$$\frac{6y}{6}=\frac{7x-5}{6}$$
$$y=\frac{7x-5}{6}$$
