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

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

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

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

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

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

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

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

Reorder the terms:
ax + -1x + (2ay + 1y) + -1 = 0
ax + -1x + (2ay + 1y) + -1 = 0

Reorder the terms:
-1 + ax + 2ay + -1x + 1y = 0

Solving
-1 + ax + 2ay + -1x + 1y = 0

Solving for variable 'a'.

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

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

Reorder the terms:
-1 + 1 + ax + 2ay + -1x + 1y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + ax + 2ay + -1x + 1y = 0 + 1
ax + 2ay + -1x + 1y = 0 + 1

Combine like terms: 0 + 1 = 1
ax + 2ay + -1x + 1y = 1

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

Combine like terms: -1x + x = 0
ax + 2ay + 0 + 1y = 1 + x
ax + 2ay + 1y = 1 + x

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

Combine like terms: 1y + -1y = 0
ax + 2ay + 0 = 1 + x + -1y
ax + 2ay = 1 + x + -1y

Reorder the terms:
-1 + ax + 2ay + -1x + y = 1 + x + -1y + -1 + -1x + y

Reorder the terms:
-1 + ax + 2ay + -1x + y = 1 + -1 + x + -1x + -1y + y

Combine like terms: 1 + -1 = 0
-1 + ax + 2ay + -1x + y = 0 + x + -1x + -1y + y
-1 + ax + 2ay + -1x + y = x + -1x + -1y + y

Combine like terms: x + -1x = 0
-1 + ax + 2ay + -1x + y = 0 + -1y + y
-1 + ax + 2ay + -1x + y = -1y + y

Combine like terms: -1y + y = 0
-1 + ax + 2ay + -1x + y = 0

The solution to this equation could not be determined.