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Simplifying y[n] = 0.2y[n + -1] + x[n] Multiply y * n ny = 0.2y[n + -1] + x[n] Reorder the terms: ny = 0.2y[-1 + n] + x[n] ny = [-1 * 0.2y + n * 0.2y] + x[n] Reorder the terms: ny = [0.2ny + -0.2y] + x[n] ny = [0.2ny + -0.2y] + x[n] Multiply x * n ny = 0.2ny + -0.2y + nx Reorder the terms: ny = nx + 0.2ny + -0.2y Solving ny = nx + 0.2ny + -0.2y 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 = nx + 0.2ny + -1nx + -0.2y Reorder the terms: -1nx + ny = nx + -1nx + 0.2ny + -0.2y Combine like terms: nx + -1nx = 0 -1nx + ny = 0 + 0.2ny + -0.2y -1nx + ny = 0.2ny + -0.2y Add '-0.2ny' to each side of the equation. -1nx + ny + -0.2ny = 0.2ny + -0.2ny + -0.2y Combine like terms: ny + -0.2ny = 0.8ny -1nx + 0.8ny = 0.2ny + -0.2ny + -0.2y Combine like terms: 0.2ny + -0.2ny = 0.0 -1nx + 0.8ny = 0.0 + -0.2y -1nx + 0.8ny = -0.2y Combine like terms: -0.2y + 0.2y = 0.0 -1nx + 0.8ny + 0.2y = 0.0 The solution to this equation could not be determined.
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