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-4x=2y+6
Add 6 to both sides.
\frac{-4x}{-4}=\frac{2y+6}{-4}
Divide both sides by -4.
x=\frac{2y+6}{-4}
Dividing by -4 undoes the multiplication by -4.
x=\frac{-y-3}{2}
Divide 6+2y by -4.
2y=-4x-6
Swap sides so that all variable terms are on the left hand side.
\frac{2y}{2}=\frac{-4x-6}{2}
Divide both sides by 2.
y=\frac{-4x-6}{2}
Dividing by 2 undoes the multiplication by 2.
y=-2x-3
Divide -4x-6 by 2.