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9x=3y-6
Subtract 6 from both sides.
\frac{9x}{9}=\frac{3y-6}{9}
Divide both sides by 9.
x=\frac{3y-6}{9}
Dividing by 9 undoes the multiplication by 9.
x=\frac{y-2}{3}
Divide -6+3y by 9.
3y=9x+6
Swap sides so that all variable terms are on the left hand side.
\frac{3y}{3}=\frac{9x+6}{3}
Divide both sides by 3.
y=\frac{9x+6}{3}
Dividing by 3 undoes the multiplication by 3.
y=3x+2
Divide 9x+6 by 3.