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Simplifying y(n) = 0.5x(n) + 0.5x(n + -1) Multiply y * n ny = 0.5x(n) + 0.5x(n + -1) Multiply x * n ny = 0.5nx + 0.5x(n + -1) Reorder the terms: ny = 0.5nx + 0.5x(-1 + n) ny = 0.5nx + (-1 * 0.5x + n * 0.5x) Reorder the terms: ny = 0.5nx + (0.5nx + -0.5x) ny = 0.5nx + (0.5nx + -0.5x) Combine like terms: 0.5nx + 0.5nx = 1nx ny = 1nx + -0.5x Solving ny = 1nx + -0.5x 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 = 1nx + -1nx + -0.5x Combine like terms: 1nx + -1nx = 0 -1nx + ny = 0 + -0.5x -1nx + ny = -0.5x Combine like terms: -0.5x + 0.5x = 0.0 -1nx + ny + 0.5x = 0.0 The solution to this equation could not be determined.
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