(3x-1)(3y-1)=1

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Solution for (3x-1)(3y-1)=1 equation: 


Simplifying
(3x + -1)(3y + -1) = 1

Reorder the terms:
(-1 + 3x)(3y + -1) = 1

Reorder the terms:
(-1 + 3x)(-1 + 3y) = 1

Multiply (-1 + 3x) * (-1 + 3y)
(-1(-1 + 3y) + 3x * (-1 + 3y)) = 1
((-1 * -1 + 3y * -1) + 3x * (-1 + 3y)) = 1
((1 + -3y) + 3x * (-1 + 3y)) = 1
(1 + -3y + (-1 * 3x + 3y * 3x)) = 1
(1 + -3y + (-3x + 9xy)) = 1

Reorder the terms:
(1 + -3x + 9xy + -3y) = 1
(1 + -3x + 9xy + -3y) = 1

Add '-1' to each side of the equation.
1 + -3x + 9xy + -1 + -3y = 1 + -1

Reorder the terms:
1 + -1 + -3x + 9xy + -3y = 1 + -1

Combine like terms: 1 + -1 = 0
0 + -3x + 9xy + -3y = 1 + -1
-3x + 9xy + -3y = 1 + -1

Combine like terms: 1 + -1 = 0
-3x + 9xy + -3y = 0

Solving
-3x + 9xy + -3y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3y' to each side of the equation.
-3x + 9xy + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
-3x + 9xy + 0 = 0 + 3y
-3x + 9xy = 0 + 3y
Remove the zero:
-3x + 9xy = 3y

Combine like terms: 3y + -3y = 0
-3x + 9xy + -3y = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1x + 3xy + -1y) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1x + 3xy + -1y)' equal to zero and attempt to solve:

Simplifying
-1x + 3xy + -1y = 0

Solving
-1x + 3xy + -1y = 0

Move all terms containing x to the left, all other terms to the right.

Add 'y' to each side of the equation.
-1x + 3xy + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-1x + 3xy + 0 = 0 + y
-1x + 3xy = 0 + y
Remove the zero:
-1x + 3xy = y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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