Solve for x
x=\frac{53-2y}{3}
Solve for y
y=\frac{53-3x}{2}
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3\left(x+1\right)+2\left(y-1\right)=54
Multiply both sides of the equation by 6, the least common multiple of 2,3.
3x+3+2\left(y-1\right)=54
Use the distributive property to multiply 3 by x+1.
3x+3+2y-2=54
Use the distributive property to multiply 2 by y-1.
3x+1+2y=54
Subtract 2 from 3 to get 1.
3x+2y=54-1
Subtract 1 from both sides.
3x+2y=53
Subtract 1 from 54 to get 53.
3x=53-2y
Subtract 2y from both sides.
\frac{3x}{3}=\frac{53-2y}{3}
Divide both sides by 3.
x=\frac{53-2y}{3}
Dividing by 3 undoes the multiplication by 3.
3\left(x+1\right)+2\left(y-1\right)=54
Multiply both sides of the equation by 6, the least common multiple of 2,3.
3x+3+2\left(y-1\right)=54
Use the distributive property to multiply 3 by x+1.
3x+3+2y-2=54
Use the distributive property to multiply 2 by y-1.
3x+1+2y=54
Subtract 2 from 3 to get 1.
1+2y=54-3x
Subtract 3x from both sides.
2y=54-3x-1
Subtract 1 from both sides.
2y=53-3x
Subtract 1 from 54 to get 53.
\frac{2y}{2}=\frac{53-3x}{2}
Divide both sides by 2.
y=\frac{53-3x}{2}
Dividing by 2 undoes the multiplication by 2.
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