(2k-1)x+(1-k)y-1=0

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Solution for (2k-1)x+(1-k)y-1=0 equation: 


Simplifying
(2k + -1) * x + (1 + -1k) * y + -1 = 0

Reorder the terms:
(-1 + 2k) * x + (1 + -1k) * y + -1 = 0

Reorder the terms for easier multiplication:
x(-1 + 2k) + (1 + -1k) * y + -1 = 0
(-1 * x + 2k * x) + (1 + -1k) * y + -1 = 0

Reorder the terms:
(2kx + -1x) + (1 + -1k) * y + -1 = 0
(2kx + -1x) + (1 + -1k) * y + -1 = 0

Reorder the terms for easier multiplication:
2kx + -1x + y(1 + -1k) + -1 = 0
2kx + -1x + (1 * y + -1k * y) + -1 = 0

Reorder the terms:
2kx + -1x + (-1ky + 1y) + -1 = 0
2kx + -1x + (-1ky + 1y) + -1 = 0

Reorder the terms:
-1 + 2kx + -1ky + -1x + 1y = 0

Solving
-1 + 2kx + -1ky + -1x + 1y = 0

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 2kx + -1ky + -1x + 1 + 1y = 0 + 1

Reorder the terms:
-1 + 1 + 2kx + -1ky + -1x + 1y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2kx + -1ky + -1x + 1y = 0 + 1
2kx + -1ky + -1x + 1y = 0 + 1

Combine like terms: 0 + 1 = 1
2kx + -1ky + -1x + 1y = 1

Add 'x' to each side of the equation.
2kx + -1ky + -1x + x + 1y = 1 + x

Combine like terms: -1x + x = 0
2kx + -1ky + 0 + 1y = 1 + x
2kx + -1ky + 1y = 1 + x

Add '-1y' to each side of the equation.
2kx + -1ky + 1y + -1y = 1 + x + -1y

Combine like terms: 1y + -1y = 0
2kx + -1ky + 0 = 1 + x + -1y
2kx + -1ky = 1 + x + -1y

Reorder the terms:
-1 + 2kx + -1ky + -1x + y = 1 + x + -1y + -1 + -1x + y

Reorder the terms:
-1 + 2kx + -1ky + -1x + y = 1 + -1 + x + -1x + -1y + y

Combine like terms: 1 + -1 = 0
-1 + 2kx + -1ky + -1x + y = 0 + x + -1x + -1y + y
-1 + 2kx + -1ky + -1x + y = x + -1x + -1y + y

Combine like terms: x + -1x = 0
-1 + 2kx + -1ky + -1x + y = 0 + -1y + y
-1 + 2kx + -1ky + -1x + y = -1y + y

Combine like terms: -1y + y = 0
-1 + 2kx + -1ky + -1x + y = 0

The solution to this equation could not be determined.

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