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Simplifying y[n] + -0.5y[n + -1] = 0.5x[n] Multiply y * n ny + -0.5y[n + -1] = 0.5x[n] Reorder the terms: ny + -0.5y[-1 + n] = 0.5x[n] ny + [-1 * -0.5y + n * -0.5y] = 0.5x[n] Reorder the terms: ny + [-0.5ny + 0.5y] = 0.5x[n] ny + [-0.5ny + 0.5y] = 0.5x[n] Combine like terms: ny + -0.5ny = 0.5ny 0.5ny + 0.5y = 0.5x[n] Multiply x * n 0.5ny + 0.5y = 0.5nx Solving 0.5ny + 0.5y = 0.5nx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5nx' to each side of the equation. 0.5ny + -0.5nx + 0.5y = 0.5nx + -0.5nx Reorder the terms: -0.5nx + 0.5ny + 0.5y = 0.5nx + -0.5nx Combine like terms: 0.5nx + -0.5nx = 0.0 -0.5nx + 0.5ny + 0.5y = 0.0 Add '-0.5y' to each side of the equation. -0.5nx + 0.5ny + 0.5y + -0.5y = 0.0 + -0.5y Combine like terms: 0.5y + -0.5y = 0.0 -0.5nx + 0.5ny + 0.0 = 0.0 + -0.5y -0.5nx + 0.5ny = 0.0 + -0.5y Remove the zero: -0.5nx + 0.5ny = -0.5y Combine like terms: -0.5y + 0.5y = 0.0 -0.5nx + 0.5ny + 0.5y = 0.0 The solution to this equation could not be determined.
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