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Simplifying y[n] = 0.5x[n] + 0.5y[n + -1] Multiply y * n ny = 0.5x[n] + 0.5y[n + -1] Multiply x * n ny = 0.5nx + 0.5y[n + -1] Reorder the terms: ny = 0.5nx + 0.5y[-1 + n] ny = 0.5nx + [-1 * 0.5y + n * 0.5y] Reorder the terms: ny = 0.5nx + [0.5ny + -0.5y] ny = 0.5nx + [0.5ny + -0.5y] Solving ny = 0.5nx + 0.5ny + -0.5y 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. -0.5nx + ny = 0.5nx + 0.5ny + -0.5nx + -0.5y Reorder the terms: -0.5nx + ny = 0.5nx + -0.5nx + 0.5ny + -0.5y Combine like terms: 0.5nx + -0.5nx = 0.0 -0.5nx + ny = 0.0 + 0.5ny + -0.5y -0.5nx + ny = 0.5ny + -0.5y Add '-0.5ny' to each side of the equation. -0.5nx + ny + -0.5ny = 0.5ny + -0.5ny + -0.5y Combine like terms: ny + -0.5ny = 0.5ny -0.5nx + 0.5ny = 0.5ny + -0.5ny + -0.5y Combine like terms: 0.5ny + -0.5ny = 0.0 -0.5nx + 0.5ny = 0.0 + -0.5y -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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