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Simplifying y[n] = x[n + -1] + 2x[n + -2] Multiply y * n ny = x[n + -1] + 2x[n + -2] Reorder the terms: ny = x[-1 + n] + 2x[n + -2] ny = [-1 * x + n * x] + 2x[n + -2] Reorder the terms: ny = [nx + -1x] + 2x[n + -2] ny = [nx + -1x] + 2x[n + -2] Reorder the terms: ny = nx + -1x + 2x[-2 + n] ny = nx + -1x + [-2 * 2x + n * 2x] Reorder the terms: ny = nx + -1x + [2nx + -4x] ny = nx + -1x + [2nx + -4x] Reorder the terms: ny = nx + 2nx + -1x + -4x Combine like terms: nx + 2nx = 3nx ny = 3nx + -1x + -4x Combine like terms: -1x + -4x = -5x ny = 3nx + -5x Solving ny = 3nx + -5x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3nx' to each side of the equation. -3nx + ny = 3nx + -3nx + -5x Combine like terms: 3nx + -3nx = 0 -3nx + ny = 0 + -5x -3nx + ny = -5x Combine like terms: -5x + 5x = 0 -3nx + ny + 5x = 0 The solution to this equation could not be determined.
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