Solve for x
x=-\frac{y}{1-9y}
y\neq 0\text{ and }y\neq \frac{1}{9}
Solve for y
y=-\frac{x}{1-9x}
x\neq 0\text{ and }x\neq \frac{1}{9}
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y+x=9xy
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of x,y.
y+x-9xy=0
Subtract 9xy from both sides.
x-9xy=-y
Subtract y from both sides. Anything subtracted from zero gives its negation.
\left(1-9y\right)x=-y
Combine all terms containing x.
\frac{\left(1-9y\right)x}{1-9y}=-\frac{y}{1-9y}
Divide both sides by 1-9y.
x=-\frac{y}{1-9y}
Dividing by 1-9y undoes the multiplication by 1-9y.
x=-\frac{y}{1-9y}\text{, }x\neq 0
Variable x cannot be equal to 0.
y+x=9xy
Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of x,y.
y+x-9xy=0
Subtract 9xy from both sides.
y-9xy=-x
Subtract x from both sides. Anything subtracted from zero gives its negation.
\left(1-9x\right)y=-x
Combine all terms containing y.
\frac{\left(1-9x\right)y}{1-9x}=-\frac{x}{1-9x}
Divide both sides by 1-9x.
y=-\frac{x}{1-9x}
Dividing by 1-9x undoes the multiplication by 1-9x.
y=-\frac{x}{1-9x}\text{, }y\neq 0
Variable y cannot be equal to 0.
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