$$\frac{3x-7}{2}-\frac{2y-8}{3}=-1$$
$x=\frac{4y-1}{9}$
$$3\left(3x-7\right)-2\left(2y-8\right)=-6$$
$$9x-21-2\left(2y-8\right)=-6$$
$$9x-21-4y+16=-6$$
$$9x-5-4y=-6$$
$$9x-4y=-6+5$$
$$9x-4y=-1$$
$$9x=-1+4y$$
$$9x=4y-1$$
$$\frac{9x}{9}=\frac{4y-1}{9}$$
$$x=\frac{4y-1}{9}$$
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$y=\frac{9x+1}{4}$
$$-5-4y=-6-9x$$
$$-4y=-6-9x+5$$
$$-4y=-1-9x$$
$$-4y=-9x-1$$
$$\frac{-4y}{-4}=\frac{-9x-1}{-4}$$
$$y=\frac{-9x-1}{-4}$$
$$y=\frac{9x+1}{4}$$
