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Simplifying 5y[n + -2] + -1y[n + -1] + 2y[n] = 2x[n + -1] Reorder the terms: 5y[-2 + n] + -1y[n + -1] + 2y[n] = 2x[n + -1] [-2 * 5y + n * 5y] + -1y[n + -1] + 2y[n] = 2x[n + -1] Reorder the terms: [5ny + -10y] + -1y[n + -1] + 2y[n] = 2x[n + -1] [5ny + -10y] + -1y[n + -1] + 2y[n] = 2x[n + -1] Reorder the terms: 5ny + -10y + -1y[-1 + n] + 2y[n] = 2x[n + -1] 5ny + -10y + [-1 * -1y + n * -1y] + 2y[n] = 2x[n + -1] Reorder the terms: 5ny + -10y + [-1ny + 1y] + 2y[n] = 2x[n + -1] 5ny + -10y + [-1ny + 1y] + 2y[n] = 2x[n + -1] Multiply y * n 5ny + -10y + -1ny + 1y + 2ny = 2x[n + -1] Reorder the terms: 5ny + -1ny + 2ny + -10y + 1y = 2x[n + -1] Combine like terms: 5ny + -1ny = 4ny 4ny + 2ny + -10y + 1y = 2x[n + -1] Combine like terms: 4ny + 2ny = 6ny 6ny + -10y + 1y = 2x[n + -1] Combine like terms: -10y + 1y = -9y 6ny + -9y = 2x[n + -1] Reorder the terms: 6ny + -9y = 2x[-1 + n] 6ny + -9y = [-1 * 2x + n * 2x] Reorder the terms: 6ny + -9y = [2nx + -2x] 6ny + -9y = [2nx + -2x] Solving 6ny + -9y = 2nx + -2x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2nx' to each side of the equation. 6ny + -2nx + -9y = 2nx + -2nx + -2x Reorder the terms: -2nx + 6ny + -9y = 2nx + -2nx + -2x Combine like terms: 2nx + -2nx = 0 -2nx + 6ny + -9y = 0 + -2x -2nx + 6ny + -9y = -2x Add '9y' to each side of the equation. -2nx + 6ny + -9y + 9y = -2x + 9y Combine like terms: -9y + 9y = 0 -2nx + 6ny + 0 = -2x + 9y -2nx + 6ny = -2x + 9y Reorder the terms: -2nx + 6ny + 2x + -9y = -2x + 2x + 9y + -9y Combine like terms: -2x + 2x = 0 -2nx + 6ny + 2x + -9y = 0 + 9y + -9y -2nx + 6ny + 2x + -9y = 9y + -9y Combine like terms: 9y + -9y = 0 -2nx + 6ny + 2x + -9y = 0 The solution to this equation could not be determined.
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