y(n)+y(n-1)=x(n-1)+x(n-2)

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

Simplifying
y(n) + y(n + -1) = x(n + -1) + x(n + -2)

Multiply y * n
ny + y(n + -1) = x(n + -1) + x(n + -2)

Reorder the terms:
ny + y(-1 + n) = x(n + -1) + x(n + -2)
ny + (-1 * y + n * y) = x(n + -1) + x(n + -2)

Reorder the terms:
ny + (ny + -1y) = x(n + -1) + x(n + -2)
ny + (ny + -1y) = x(n + -1) + x(n + -2)

Combine like terms: ny + ny = 2ny
2ny + -1y = x(n + -1) + x(n + -2)

Reorder the terms:
2ny + -1y = x(-1 + n) + x(n + -2)
2ny + -1y = (-1 * x + n * x) + x(n + -2)

Reorder the terms:
2ny + -1y = (nx + -1x) + x(n + -2)
2ny + -1y = (nx + -1x) + x(n + -2)

Reorder the terms:
2ny + -1y = nx + -1x + x(-2 + n)
2ny + -1y = nx + -1x + (-2 * x + n * x)

Reorder the terms:
2ny + -1y = nx + -1x + (nx + -2x)
2ny + -1y = nx + -1x + (nx + -2x)

Reorder the terms:
2ny + -1y = nx + nx + -1x + -2x

Combine like terms: nx + nx = 2nx
2ny + -1y = 2nx + -1x + -2x

Combine like terms: -1x + -2x = -3x
2ny + -1y = 2nx + -3x

Solving
2ny + -1y = 2nx + -3x

Solving for variable 'n'.

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

Add '-2nx' to each side of the equation.
2ny + -2nx + -1y = 2nx + -2nx + -3x

Reorder the terms:
-2nx + 2ny + -1y = 2nx + -2nx + -3x

Combine like terms: 2nx + -2nx = 0
-2nx + 2ny + -1y = 0 + -3x
-2nx + 2ny + -1y = -3x

Add 'y' to each side of the equation.
-2nx + 2ny + -1y + y = -3x + y

Combine like terms: -1y + y = 0
-2nx + 2ny + 0 = -3x + y
-2nx + 2ny = -3x + y

Reorder the terms:
-2nx + 2ny + 3x + -1y = -3x + 3x + y + -1y

Combine like terms: -3x + 3x = 0
-2nx + 2ny + 3x + -1y = 0 + y + -1y
-2nx + 2ny + 3x + -1y = y + -1y

Combine like terms: y + -1y = 0
-2nx + 2ny + 3x + -1y = 0

The solution to this equation could not be determined.