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6x+8=-y
Subtract y from both sides. Anything subtracted from zero gives its negation.
6x=-y-8
Subtract 8 from both sides.
\frac{6x}{6}=\frac{-y-8}{6}
Divide both sides by 6.
x=\frac{-y-8}{6}
Dividing by 6 undoes the multiplication by 6.
x=-\frac{y}{6}-\frac{4}{3}
Divide -y-8 by 6.
y+8=-6x
Subtract 6x from both sides. Anything subtracted from zero gives its negation.
y=-6x-8
Subtract 8 from both sides.