Solve for x
x=-\frac{2}{3}+\frac{1}{3y}
y\neq 0
Solve for y
y=\frac{1}{3x+2}
x\neq -\frac{2}{3}
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1=y\left(3x+2\right)
Variable x cannot be equal to -\frac{2}{3} since division by zero is not defined. Multiply both sides of the equation by 3x+2.
1=3yx+2y
Use the distributive property to multiply y by 3x+2.
3yx+2y=1
Swap sides so that all variable terms are on the left hand side.
3yx=1-2y
Subtract 2y from both sides.
\frac{3yx}{3y}=\frac{1-2y}{3y}
Divide both sides by 3y.
x=\frac{1-2y}{3y}
Dividing by 3y undoes the multiplication by 3y.
x=-\frac{2}{3}+\frac{1}{3y}
Divide 1-2y by 3y.
x=-\frac{2}{3}+\frac{1}{3y}\text{, }x\neq -\frac{2}{3}
Variable x cannot be equal to -\frac{2}{3}.
1=y\left(3x+2\right)
Multiply both sides of the equation by 3x+2.
1=3yx+2y
Use the distributive property to multiply y by 3x+2.
3yx+2y=1
Swap sides so that all variable terms are on the left hand side.
\left(3x+2\right)y=1
Combine all terms containing y.
\frac{\left(3x+2\right)y}{3x+2}=\frac{1}{3x+2}
Divide both sides by 2+3x.
y=\frac{1}{3x+2}
Dividing by 2+3x undoes the multiplication by 2+3x.
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