Interchange the x and y-variables and solve for y.

$\displaystyle x=9(6y-2)$

Distribute the nine through the binomial.

$\displaystyle x=9(6y)+9(-2) = 54y-18$

$\displaystyle x= 54y-18$

Add eighteen on both sides.

$\displaystyle x+(18)= 54y-18+(18)$

$\displaystyle x+18=54y$

Divide by 54 on both sides.

$\displaystyle \frac{x+18}{54}=\frac{54y}{54}$

The answer is:  $\displaystyle y=\frac{1}{54}x+\frac{1}{3}$

Interchange the x and y-variables and solve for y.

$\displaystyle x=2(9-2y)$

Distribute the integer through the binomial.

$\displaystyle x=2(9-2y) = 18-4y$

$\displaystyle x= 18-4y$

Add $\displaystyle 4y$ on both sides.

$\displaystyle x+(4y)= 18-4y+(4y)$

$\displaystyle x+4y=18$

Subtract $\displaystyle x$ on both sides.

$\displaystyle 4y=-x+18$

Divide by four on both sides.

$\displaystyle \frac{4y}{4}=\frac{-x+18}{4}$

Simplify both sides.

The inverse is:  $\displaystyle y=-\frac{1}{4}x+\frac{9}{2}$

Interchange the x and y-variable.

$\displaystyle x=-3y-20$

Add twenty on both sides.

$\displaystyle x+20=-3y-20+20$

$\displaystyle x+20=-3y$

Divide both sides by negative three.

$\displaystyle \frac{x+20}{-3}=\frac{-3y}{-3}$

Simplify both sides of the equation.

The answer is:  $\displaystyle y=-\frac{1}{3}x-\frac{20}{3}$

Interchange the x and y-values.

$\displaystyle x=-9y-5$

Solve for y.  Add five on both sides.

$\displaystyle x+(5)=-9y-5+(5)$

The equation becomes:  $\displaystyle x+5 =-9y$

Divide by negative nine on both sides.

$\displaystyle \frac{x+5}{-9} =\frac{-9y}{-9}$

The answer is:  $\displaystyle y= -\frac{1}{9}x-\frac{5}{9}$

Interchange both the x and y- variables.

$\displaystyle x=3(y-10)$

Solve for y.  Distribute the three through both terms of the binomial.

$\displaystyle x=3y-30$

Add 30 on both sides.

$\displaystyle x+30=3y-30+30$

$\displaystyle x+30=3y$

Divide by three on both sides.

$\displaystyle \frac{x+30}{3}=\frac{3y}{3}$

Simplify both sides.

The answer is:  $\displaystyle y=\frac{1}{3}x+10$

Interchange the x and y-variables.

$\displaystyle x=9y+26$

Solve for y.  Subtract 26 from both sides.

$\displaystyle x-26=9y+26-26$

The equation becomes:

$\displaystyle x-26=9y$

Divide by nine on both sides.

$\displaystyle \frac{x-26}{9}=\frac{9y}{9}$

Simplify both fractions.

The answer is:  $\displaystyle y=\frac{1}{9}x-\frac{26}{9}$

Interchange the x and y variables and solve for y.

$\displaystyle x= 7y-4$

Add four on both sides.

$\displaystyle x+4= 7y-4+4$

Simplify both sides.

$\displaystyle x+4= 7y$

Divide by seven on both sides.

$\displaystyle \frac{x+4}{7}= \frac{7y}{7}$

The answer is:  $\displaystyle y=\frac{1}{7}x+\frac{4}{7}$

In order to determine the inverse, interchange the x and y-variables.

$\displaystyle x=-(y+6)$

Divide by negative one on both sides.

$\displaystyle \frac{x}{-1}=\frac{-(y+6)}{-1}$

Simplify both sides.

$\displaystyle -x = y+6$

Subtract six from both sides.

$\displaystyle -x-6 = y+6-6$

The answer is:  $\displaystyle y=-x-6$

Interchange the x and y-variables.

$\displaystyle x= 2y-50$

Add 50 on both sides.

$\displaystyle x+50= 2y-50+50$

The equation becomes: 

$\displaystyle x+50= 2y$

Divide both sides by two and split the fraction.

$\displaystyle \frac{x+50}{2}=\frac{ 2y}{2}$

The answer is:  $\displaystyle y=\frac{1}{2}x+25$

Interchange the x and y-variables.

$\displaystyle x=-4y-19$

Add 19 on both sides.

$\displaystyle x+19=-4y-19+19$

$\displaystyle x+19=-4y$

Divide by negative four on both sides.

$\displaystyle \frac{x+19}{-4}=\frac{-4y}{-4}$

Simplify both sides.

The answer is:  $\displaystyle -\frac{1}{4}x-\frac{19}{4}$