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