y(n)=0.7y(n-1)-0.1y(n-2)+2x(n)-x(n-2)

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Solution for y(n)=0.7y(n-1)-0.1y(n-2)+2x(n)-x(n-2) equation: 


Simplifying
y(n) = 0.7y(n + -1) + -0.1y(n + -2) + 2x(n) + -1x(n + -2)

Multiply y * n
ny = 0.7y(n + -1) + -0.1y(n + -2) + 2x(n) + -1x(n + -2)

Reorder the terms:
ny = 0.7y(-1 + n) + -0.1y(n + -2) + 2x(n) + -1x(n + -2)
ny = (-1 * 0.7y + n * 0.7y) + -0.1y(n + -2) + 2x(n) + -1x(n + -2)

Reorder the terms:
ny = (0.7ny + -0.7y) + -0.1y(n + -2) + 2x(n) + -1x(n + -2)
ny = (0.7ny + -0.7y) + -0.1y(n + -2) + 2x(n) + -1x(n + -2)

Reorder the terms:
ny = 0.7ny + -0.7y + -0.1y(-2 + n) + 2x(n) + -1x(n + -2)
ny = 0.7ny + -0.7y + (-2 * -0.1y + n * -0.1y) + 2x(n) + -1x(n + -2)

Reorder the terms:
ny = 0.7ny + -0.7y + (-0.1ny + 0.2y) + 2x(n) + -1x(n + -2)
ny = 0.7ny + -0.7y + (-0.1ny + 0.2y) + 2x(n) + -1x(n + -2)

Multiply x * n
ny = 0.7ny + -0.7y + -0.1ny + 0.2y + 2nx + -1x(n + -2)

Reorder the terms:
ny = 0.7ny + -0.7y + -0.1ny + 0.2y + 2nx + -1x(-2 + n)
ny = 0.7ny + -0.7y + -0.1ny + 0.2y + 2nx + (-2 * -1x + n * -1x)

Reorder the terms:
ny = 0.7ny + -0.7y + -0.1ny + 0.2y + 2nx + (-1nx + 2x)
ny = 0.7ny + -0.7y + -0.1ny + 0.2y + 2nx + (-1nx + 2x)

Reorder the terms:
ny = 2nx + -1nx + 0.7ny + -0.1ny + 2x + -0.7y + 0.2y

Combine like terms: 2nx + -1nx = 1nx
ny = 1nx + 0.7ny + -0.1ny + 2x + -0.7y + 0.2y

Combine like terms: 0.7ny + -0.1ny = 0.6ny
ny = 1nx + 0.6ny + 2x + -0.7y + 0.2y

Combine like terms: -0.7y + 0.2y = -0.5y
ny = 1nx + 0.6ny + 2x + -0.5y

Solving
ny = 1nx + 0.6ny + 2x + -0.5y

Solving for variable 'n'.

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

Add '-1nx' to each side of the equation.
-1nx + ny = 1nx + 0.6ny + 2x + -1nx + -0.5y

Reorder the terms:
-1nx + ny = 1nx + -1nx + 0.6ny + 2x + -0.5y

Combine like terms: 1nx + -1nx = 0
-1nx + ny = 0 + 0.6ny + 2x + -0.5y
-1nx + ny = 0.6ny + 2x + -0.5y

Add '-0.6ny' to each side of the equation.
-1nx + ny + -0.6ny = 0.6ny + 2x + -0.6ny + -0.5y

Combine like terms: ny + -0.6ny = 0.4ny
-1nx + 0.4ny = 0.6ny + 2x + -0.6ny + -0.5y

Reorder the terms:
-1nx + 0.4ny = 0.6ny + -0.6ny + 2x + -0.5y

Combine like terms: 0.6ny + -0.6ny = 0.0
-1nx + 0.4ny = 0.0 + 2x + -0.5y
-1nx + 0.4ny = 2x + -0.5y

Reorder the terms:
-1nx + 0.4ny + -2x + 0.5y = 2x + -2x + -0.5y + 0.5y

Combine like terms: 2x + -2x = 0
-1nx + 0.4ny + -2x + 0.5y = 0 + -0.5y + 0.5y
-1nx + 0.4ny + -2x + 0.5y = -0.5y + 0.5y

Combine like terms: -0.5y + 0.5y = 0.0
-1nx + 0.4ny + -2x + 0.5y = 0.0

The solution to this equation could not be determined.

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