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6x=-2y
Subtract 2y from both sides. Anything subtracted from zero gives its negation.
\frac{6x}{6}=-\frac{2y}{6}
Divide both sides by 6.
x=-\frac{2y}{6}
Dividing by 6 undoes the multiplication by 6.
x=-\frac{y}{3}
Divide -2y by 6.
2y=-6x
Subtract 6x from both sides. Anything subtracted from zero gives its negation.
\frac{2y}{2}=-\frac{6x}{2}
Divide both sides by 2.
y=-\frac{6x}{2}
Dividing by 2 undoes the multiplication by 2.
y=-3x
Divide -6x by 2.