Solve for x
x=\frac{13y}{9}
y\neq 0
Solve for y
y=\frac{9x}{13}
x\neq 0
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9x=13y
Multiply both sides of the equation by 9y, the least common multiple of y,9.
\frac{9x}{9}=\frac{13y}{9}
Divide both sides by 9.
x=\frac{13y}{9}
Dividing by 9 undoes the multiplication by 9.
9x=13y
Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 9y, the least common multiple of y,9.
13y=9x
Swap sides so that all variable terms are on the left hand side.
\frac{13y}{13}=\frac{9x}{13}
Divide both sides by 13.
y=\frac{9x}{13}
Dividing by 13 undoes the multiplication by 13.
y=\frac{9x}{13}\text{, }y\neq 0
Variable y cannot be equal to 0.
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