Solve for x
x=\frac{3y}{2}
Solve for y
y=\frac{2x}{3}
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3\left(20+2y\right)=2\left(30+2x\right)
Multiply both sides of the equation by 60, the least common multiple of 20,30.
60+6y=2\left(30+2x\right)
Use the distributive property to multiply 3 by 20+2y.
60+6y=60+4x
Use the distributive property to multiply 2 by 30+2x.
60+4x=60+6y
Swap sides so that all variable terms are on the left hand side.
4x=60+6y-60
Subtract 60 from both sides.
4x=6y
Subtract 60 from 60 to get 0.
\frac{4x}{4}=\frac{6y}{4}
Divide both sides by 4.
x=\frac{6y}{4}
Dividing by 4 undoes the multiplication by 4.
x=\frac{3y}{2}
Divide 6y by 4.
3\left(20+2y\right)=2\left(30+2x\right)
Multiply both sides of the equation by 60, the least common multiple of 20,30.
60+6y=2\left(30+2x\right)
Use the distributive property to multiply 3 by 20+2y.
60+6y=60+4x
Use the distributive property to multiply 2 by 30+2x.
6y=60+4x-60
Subtract 60 from both sides.
6y=4x
Subtract 60 from 60 to get 0.
\frac{6y}{6}=\frac{4x}{6}
Divide both sides by 6.
y=\frac{4x}{6}
Dividing by 6 undoes the multiplication by 6.
y=\frac{2x}{3}
Divide 4x by 6.
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