Solve for x
x=6-\frac{3}{y}
y\neq 0
Solve for y
y=-\frac{3}{x-6}
x\neq 6
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3=y\left(-1\right)x+3y\times 2
Multiply both sides of the equation by 3y, the least common multiple of y,3.
3=y\left(-1\right)x+6y
Multiply 3 and 2 to get 6.
y\left(-1\right)x+6y=3
Swap sides so that all variable terms are on the left hand side.
y\left(-1\right)x=3-6y
Subtract 6y from both sides.
\left(-y\right)x=3-6y
The equation is in standard form.
\frac{\left(-y\right)x}{-y}=\frac{3-6y}{-y}
Divide both sides by -y.
x=\frac{3-6y}{-y}
Dividing by -y undoes the multiplication by -y.
x=6-\frac{3}{y}
Divide 3-6y by -y.
3=y\left(-1\right)x+3y\times 2
Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3y, the least common multiple of y,3.
3=y\left(-1\right)x+6y
Multiply 3 and 2 to get 6.
y\left(-1\right)x+6y=3
Swap sides so that all variable terms are on the left hand side.
\left(-x+6\right)y=3
Combine all terms containing y.
\left(6-x\right)y=3
The equation is in standard form.
\frac{\left(6-x\right)y}{6-x}=\frac{3}{6-x}
Divide both sides by -x+6.
y=\frac{3}{6-x}
Dividing by -x+6 undoes the multiplication by -x+6.
y=\frac{3}{6-x}\text{, }y\neq 0
Variable y cannot be equal to 0.
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