y[n]=0.7*y[n-1]+0.3*u[n-1]

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Solution for y[n]=0.7*y[n-1]+0.3*u[n-1] equation: 


Simplifying
y[n] = 0.7y[n + -1] + 0.3u[n + -1]

Multiply y * n
ny = 0.7y[n + -1] + 0.3u[n + -1]

Reorder the terms:
ny = 0.7y[-1 + n] + 0.3u[n + -1]
ny = [-1 * 0.7y + n * 0.7y] + 0.3u[n + -1]

Reorder the terms:
ny = [0.7ny + -0.7y] + 0.3u[n + -1]
ny = [0.7ny + -0.7y] + 0.3u[n + -1]

Reorder the terms:
ny = 0.7ny + -0.7y + 0.3u[-1 + n]
ny = 0.7ny + -0.7y + [-1 * 0.3u + n * 0.3u]

Reorder the terms:
ny = 0.7ny + -0.7y + [0.3nu + -0.3u]
ny = 0.7ny + -0.7y + [0.3nu + -0.3u]

Reorder the terms:
ny = 0.3nu + 0.7ny + -0.3u + -0.7y

Solving
ny = 0.3nu + 0.7ny + -0.3u + -0.7y

Solving for variable 'n'.

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

Add '-0.3nu' to each side of the equation.
-0.3nu + ny = 0.3nu + 0.7ny + -0.3u + -0.3nu + -0.7y

Reorder the terms:
-0.3nu + ny = 0.3nu + -0.3nu + 0.7ny + -0.3u + -0.7y

Combine like terms: 0.3nu + -0.3nu = 0.0
-0.3nu + ny = 0.0 + 0.7ny + -0.3u + -0.7y
-0.3nu + ny = 0.7ny + -0.3u + -0.7y

Add '-0.7ny' to each side of the equation.
-0.3nu + ny + -0.7ny = 0.7ny + -0.3u + -0.7ny + -0.7y

Combine like terms: ny + -0.7ny = 0.3ny
-0.3nu + 0.3ny = 0.7ny + -0.3u + -0.7ny + -0.7y

Reorder the terms:
-0.3nu + 0.3ny = 0.7ny + -0.7ny + -0.3u + -0.7y

Combine like terms: 0.7ny + -0.7ny = 0.0
-0.3nu + 0.3ny = 0.0 + -0.3u + -0.7y
-0.3nu + 0.3ny = -0.3u + -0.7y

Reorder the terms:
-0.3nu + 0.3ny + 0.3u + 0.7y = -0.3u + 0.3u + -0.7y + 0.7y

Combine like terms: -0.3u + 0.3u = 0.0
-0.3nu + 0.3ny + 0.3u + 0.7y = 0.0 + -0.7y + 0.7y
-0.3nu + 0.3ny + 0.3u + 0.7y = -0.7y + 0.7y

Combine like terms: -0.7y + 0.7y = 0.0
-0.3nu + 0.3ny + 0.3u + 0.7y = 0.0

The solution to this equation could not be determined.

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