$$15(x-y)-3(x-9)+5(x+6)=0$$
$x=\frac{15y-57}{17}$
$$15x-15y-3\left(x-9\right)+5\left(x+6\right)=0$$
$$15x-15y-3x+27+5\left(x+6\right)=0$$
$$12x-15y+27+5\left(x+6\right)=0$$
$$12x-15y+27+5x+30=0$$
$$17x-15y+27+30=0$$
$$17x-15y+57=0$$
$$17x+57=15y$$
$$17x=15y-57$$
$$\frac{17x}{17}=\frac{15y-57}{17}$$
$$x=\frac{15y-57}{17}$$
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$y=\frac{17x}{15}+\frac{19}{5}$
$$-15y+57=-17x$$
$$-15y=-17x-57$$
$$\frac{-15y}{-15}=\frac{-17x-57}{-15}$$
$$y=\frac{-17x-57}{-15}$$
$$y=\frac{17x}{15}+\frac{19}{5}$$
