y(n)-0.5y(n-1)=x(n)+x(n-1)

Solution for y(n)-0.5y(n-1)=x(n)+x(n-1) equation:

Simplifying
y(n) + -0.5y(n + -1) = x(n) + x(n + -1)

Multiply y * n
ny + -0.5y(n + -1) = x(n) + x(n + -1)

Reorder the terms:
ny + -0.5y(-1 + n) = x(n) + x(n + -1)
ny + (-1 * -0.5y + n * -0.5y) = x(n) + x(n + -1)

Reorder the terms:
ny + (-0.5ny + 0.5y) = x(n) + x(n + -1)
ny + (-0.5ny + 0.5y) = x(n) + x(n + -1)

Combine like terms: ny + -0.5ny = 0.5ny
0.5ny + 0.5y = x(n) + x(n + -1)

Multiply x * n
0.5ny + 0.5y = nx + x(n + -1)

Reorder the terms:
0.5ny + 0.5y = nx + x(-1 + n)
0.5ny + 0.5y = nx + (-1 * x + n * x)

Reorder the terms:
0.5ny + 0.5y = nx + (nx + -1x)
0.5ny + 0.5y = nx + (nx + -1x)

Combine like terms: nx + nx = 2nx
0.5ny + 0.5y = 2nx + -1x

Solving
0.5ny + 0.5y = 2nx + -1x

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.
0.5ny + -2nx + 0.5y = 2nx + -2nx + -1x

Reorder the terms:
-2nx + 0.5ny + 0.5y = 2nx + -2nx + -1x

Combine like terms: 2nx + -2nx = 0
-2nx + 0.5ny + 0.5y = 0 + -1x
-2nx + 0.5ny + 0.5y = -1x

Add '-0.5y' to each side of the equation.
-2nx + 0.5ny + 0.5y + -0.5y = -1x + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
-2nx + 0.5ny + 0.0 = -1x + -0.5y
-2nx + 0.5ny = -1x + -0.5y

Reorder the terms:
-2nx + 0.5ny + x + 0.5y = -1x + x + -0.5y + 0.5y

Combine like terms: -1x + x = 0
-2nx + 0.5ny + x + 0.5y = 0 + -0.5y + 0.5y
-2nx + 0.5ny + x + 0.5y = -0.5y + 0.5y

Combine like terms: -0.5y + 0.5y = 0.0
-2nx + 0.5ny + x + 0.5y = 0.0

The solution to this equation could not be determined.