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Simplifying y[n] + -0.5y[n + -1] + 0.1y[n + -2] = x[n] Multiply y * n ny + -0.5y[n + -1] + 0.1y[n + -2] = x[n] Reorder the terms: ny + -0.5y[-1 + n] + 0.1y[n + -2] = x[n] ny + [-1 * -0.5y + n * -0.5y] + 0.1y[n + -2] = x[n] Reorder the terms: ny + [-0.5ny + 0.5y] + 0.1y[n + -2] = x[n] ny + [-0.5ny + 0.5y] + 0.1y[n + -2] = x[n] Reorder the terms: ny + -0.5ny + 0.5y + 0.1y[-2 + n] = x[n] ny + -0.5ny + 0.5y + [-2 * 0.1y + n * 0.1y] = x[n] Reorder the terms: ny + -0.5ny + 0.5y + [0.1ny + -0.2y] = x[n] ny + -0.5ny + 0.5y + [0.1ny + -0.2y] = x[n] Reorder the terms: ny + -0.5ny + 0.1ny + 0.5y + -0.2y = x[n] Combine like terms: ny + -0.5ny = 0.5ny 0.5ny + 0.1ny + 0.5y + -0.2y = x[n] Combine like terms: 0.5ny + 0.1ny = 0.6ny 0.6ny + 0.5y + -0.2y = x[n] Combine like terms: 0.5y + -0.2y = 0.3y 0.6ny + 0.3y = x[n] Multiply x * n 0.6ny + 0.3y = nx Solving 0.6ny + 0.3y = nx 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. 0.6ny + -1nx + 0.3y = nx + -1nx Reorder the terms: -1nx + 0.6ny + 0.3y = nx + -1nx Combine like terms: nx + -1nx = 0 -1nx + 0.6ny + 0.3y = 0 Add '-0.3y' to each side of the equation. -1nx + 0.6ny + 0.3y + -0.3y = 0 + -0.3y Combine like terms: 0.3y + -0.3y = 0.0 -1nx + 0.6ny + 0.0 = 0 + -0.3y -1nx + 0.6ny = 0 + -0.3y Remove the zero: -1nx + 0.6ny = -0.3y Combine like terms: -0.3y + 0.3y = 0.0 -1nx + 0.6ny + 0.3y = 0.0 The solution to this equation could not be determined.
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