Solve for x
x=\frac{8\left(y-3\right)}{9}
Solve for y
y=\frac{9x}{8}+3
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3\left(3x+4\right)=2\left(4y-6\right)
Multiply both sides of the equation by 12, the least common multiple of 4,6.
9x+12=2\left(4y-6\right)
Use the distributive property to multiply 3 by 3x+4.
9x+12=8y-12
Use the distributive property to multiply 2 by 4y-6.
9x=8y-12-12
Subtract 12 from both sides.
9x=8y-24
Subtract 12 from -12 to get -24.
\frac{9x}{9}=\frac{8y-24}{9}
Divide both sides by 9.
x=\frac{8y-24}{9}
Dividing by 9 undoes the multiplication by 9.
x=\frac{8y}{9}-\frac{8}{3}
Divide -24+8y by 9.
3\left(3x+4\right)=2\left(4y-6\right)
Multiply both sides of the equation by 12, the least common multiple of 4,6.
9x+12=2\left(4y-6\right)
Use the distributive property to multiply 3 by 3x+4.
9x+12=8y-12
Use the distributive property to multiply 2 by 4y-6.
8y-12=9x+12
Swap sides so that all variable terms are on the left hand side.
8y=9x+12+12
Add 12 to both sides.
8y=9x+24
Add 12 and 12 to get 24.
\frac{8y}{8}=\frac{9x+24}{8}
Divide both sides by 8.
y=\frac{9x+24}{8}
Dividing by 8 undoes the multiplication by 8.
y=\frac{9x}{8}+3
Divide 9x+24 by 8.
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