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2x+2z=2+3y
Add 3y to both sides.
2x=2+3y-2z
Subtract 2z from both sides.
2x=3y-2z+2
The equation is in standard form.
\frac{2x}{2}=\frac{3y-2z+2}{2}
Divide both sides by 2.
x=\frac{3y-2z+2}{2}
Dividing by 2 undoes the multiplication by 2.
x=\frac{3y}{2}-z+1
Divide 2+3y-2z by 2.
-3y+2z=2-2x
Subtract 2x from both sides.
-3y=2-2x-2z
Subtract 2z from both sides.
-3y=2-2z-2x
The equation is in standard form.
\frac{-3y}{-3}=\frac{2-2z-2x}{-3}
Divide both sides by -3.
y=\frac{2-2z-2x}{-3}
Dividing by -3 undoes the multiplication by -3.
y=\frac{2x+2z-2}{3}
Divide 2-2x-2z by -3.