Solve for x
x=-\frac{3y+7}{1-y}
y\neq 1
Solve for y
y=-\frac{x+7}{3-x}
x\neq 3
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x+7=y\left(x-3\right)
Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.
x+7=yx-3y
Use the distributive property to multiply y by x-3.
x+7-yx=-3y
Subtract yx from both sides.
x-yx=-3y-7
Subtract 7 from both sides.
\left(1-y\right)x=-3y-7
Combine all terms containing x.
\frac{\left(1-y\right)x}{1-y}=\frac{-3y-7}{1-y}
Divide both sides by -y+1.
x=\frac{-3y-7}{1-y}
Dividing by -y+1 undoes the multiplication by -y+1.
x=-\frac{3y+7}{1-y}
Divide -3y-7 by -y+1.
x=-\frac{3y+7}{1-y}\text{, }x\neq 3
Variable x cannot be equal to 3.
x+7=y\left(x-3\right)
Multiply both sides of the equation by x-3.
x+7=yx-3y
Use the distributive property to multiply y by x-3.
yx-3y=x+7
Swap sides so that all variable terms are on the left hand side.
\left(x-3\right)y=x+7
Combine all terms containing y.
\frac{\left(x-3\right)y}{x-3}=\frac{x+7}{x-3}
Divide both sides by x-3.
y=\frac{x+7}{x-3}
Dividing by x-3 undoes the multiplication by x-3.
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