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Simplifying y[n + 2] + -5y[n + 1] + 6y[n] = 3x[n + 1] + 5x[n] Reorder the terms: y[2 + n] + -5y[n + 1] + 6y[n] = 3x[n + 1] + 5x[n] [2 * y + n * y] + -5y[n + 1] + 6y[n] = 3x[n + 1] + 5x[n] Reorder the terms: [ny + 2y] + -5y[n + 1] + 6y[n] = 3x[n + 1] + 5x[n] [ny + 2y] + -5y[n + 1] + 6y[n] = 3x[n + 1] + 5x[n] Reorder the terms: ny + 2y + -5y[1 + n] + 6y[n] = 3x[n + 1] + 5x[n] ny + 2y + [1 * -5y + n * -5y] + 6y[n] = 3x[n + 1] + 5x[n] Reorder the terms: ny + 2y + [-5ny + -5y] + 6y[n] = 3x[n + 1] + 5x[n] ny + 2y + [-5ny + -5y] + 6y[n] = 3x[n + 1] + 5x[n] Multiply y * n ny + 2y + -5ny + -5y + 6ny = 3x[n + 1] + 5x[n] Reorder the terms: ny + -5ny + 6ny + 2y + -5y = 3x[n + 1] + 5x[n] Combine like terms: ny + -5ny = -4ny -4ny + 6ny + 2y + -5y = 3x[n + 1] + 5x[n] Combine like terms: -4ny + 6ny = 2ny 2ny + 2y + -5y = 3x[n + 1] + 5x[n] Combine like terms: 2y + -5y = -3y 2ny + -3y = 3x[n + 1] + 5x[n] Reorder the terms: 2ny + -3y = 3x[1 + n] + 5x[n] 2ny + -3y = [1 * 3x + n * 3x] + 5x[n] Reorder the terms: 2ny + -3y = [3nx + 3x] + 5x[n] 2ny + -3y = [3nx + 3x] + 5x[n] Multiply x * n 2ny + -3y = 3nx + 3x + 5nx Reorder the terms: 2ny + -3y = 3nx + 5nx + 3x Combine like terms: 3nx + 5nx = 8nx 2ny + -3y = 8nx + 3x Solving 2ny + -3y = 8nx + 3x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8nx' to each side of the equation. 2ny + -8nx + -3y = 8nx + -8nx + 3x Reorder the terms: -8nx + 2ny + -3y = 8nx + -8nx + 3x Combine like terms: 8nx + -8nx = 0 -8nx + 2ny + -3y = 0 + 3x -8nx + 2ny + -3y = 3x Add '3y' to each side of the equation. -8nx + 2ny + -3y + 3y = 3x + 3y Combine like terms: -3y + 3y = 0 -8nx + 2ny + 0 = 3x + 3y -8nx + 2ny = 3x + 3y Reorder the terms: -8nx + 2ny + -3x + -3y = 3x + -3x + 3y + -3y Combine like terms: 3x + -3x = 0 -8nx + 2ny + -3x + -3y = 0 + 3y + -3y -8nx + 2ny + -3x + -3y = 3y + -3y Combine like terms: 3y + -3y = 0 -8nx + 2ny + -3x + -3y = 0 The solution to this equation could not be determined.
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