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Simplifying y[n] = 0.25y[n + -2] + x[n] Multiply y * n ny = 0.25y[n + -2] + x[n] Reorder the terms: ny = 0.25y[-2 + n] + x[n] ny = [-2 * 0.25y + n * 0.25y] + x[n] Reorder the terms: ny = [0.25ny + -0.5y] + x[n] ny = [0.25ny + -0.5y] + x[n] Multiply x * n ny = 0.25ny + -0.5y + nx Reorder the terms: ny = nx + 0.25ny + -0.5y Solving ny = nx + 0.25ny + -0.5y 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 + 0.25ny + -1nx + -0.5y Reorder the terms: -1nx + ny = nx + -1nx + 0.25ny + -0.5y Combine like terms: nx + -1nx = 0 -1nx + ny = 0 + 0.25ny + -0.5y -1nx + ny = 0.25ny + -0.5y Add '-0.25ny' to each side of the equation. -1nx + ny + -0.25ny = 0.25ny + -0.25ny + -0.5y Combine like terms: ny + -0.25ny = 0.75ny -1nx + 0.75ny = 0.25ny + -0.25ny + -0.5y Combine like terms: 0.25ny + -0.25ny = 0.00 -1nx + 0.75ny = 0.00 + -0.5y -1nx + 0.75ny = -0.5y Combine like terms: -0.5y + 0.5y = 0.0 -1nx + 0.75ny + 0.5y = 0.0 The solution to this equation could not be determined.
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