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Simplifying y[n] = x[n] + -0.25y[n + -2] Multiply y * n ny = x[n] + -0.25y[n + -2] Multiply x * n ny = nx + -0.25y[n + -2] Reorder the terms: ny = nx + -0.25y[-2 + n] ny = nx + [-2 * -0.25y + n * -0.25y] Reorder the terms: ny = nx + [-0.25ny + 0.5y] 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 = 1.25ny -1nx + 1.25ny = -0.25ny + 0.25ny + 0.5y Combine like terms: -0.25ny + 0.25ny = 0.00 -1nx + 1.25ny = 0.00 + 0.5y -1nx + 1.25ny = 0.5y Combine like terms: 0.5y + -0.5y = 0.0 -1nx + 1.25ny + -0.5y = 0.0 The solution to this equation could not be determined.
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