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