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