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Simplifying y(n) + 0.6y(n + -1) + 0.08y(n + -2) = x(n) + 0.5x(n + -1) Multiply y * n ny + 0.6y(n + -1) + 0.08y(n + -2) = x(n) + 0.5x(n + -1) Reorder the terms: ny + 0.6y(-1 + n) + 0.08y(n + -2) = x(n) + 0.5x(n + -1) ny + (-1 * 0.6y + n * 0.6y) + 0.08y(n + -2) = x(n) + 0.5x(n + -1) Reorder the terms: ny + (0.6ny + -0.6y) + 0.08y(n + -2) = x(n) + 0.5x(n + -1) ny + (0.6ny + -0.6y) + 0.08y(n + -2) = x(n) + 0.5x(n + -1) Reorder the terms: ny + 0.6ny + -0.6y + 0.08y(-2 + n) = x(n) + 0.5x(n + -1) ny + 0.6ny + -0.6y + (-2 * 0.08y + n * 0.08y) = x(n) + 0.5x(n + -1) Reorder the terms: ny + 0.6ny + -0.6y + (0.08ny + -0.16y) = x(n) + 0.5x(n + -1) ny + 0.6ny + -0.6y + (0.08ny + -0.16y) = x(n) + 0.5x(n + -1) Reorder the terms: ny + 0.6ny + 0.08ny + -0.6y + -0.16y = x(n) + 0.5x(n + -1) Combine like terms: ny + 0.6ny = 1.6ny 1.6ny + 0.08ny + -0.6y + -0.16y = x(n) + 0.5x(n + -1) Combine like terms: 1.6ny + 0.08ny = 1.68ny 1.68ny + -0.6y + -0.16y = x(n) + 0.5x(n + -1) Combine like terms: -0.6y + -0.16y = -0.76y 1.68ny + -0.76y = x(n) + 0.5x(n + -1) Multiply x * n 1.68ny + -0.76y = nx + 0.5x(n + -1) Reorder the terms: 1.68ny + -0.76y = nx + 0.5x(-1 + n) 1.68ny + -0.76y = nx + (-1 * 0.5x + n * 0.5x) Reorder the terms: 1.68ny + -0.76y = nx + (0.5nx + -0.5x) 1.68ny + -0.76y = nx + (0.5nx + -0.5x) Combine like terms: nx + 0.5nx = 1.5nx 1.68ny + -0.76y = 1.5nx + -0.5x Solving 1.68ny + -0.76y = 1.5nx + -0.5x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5nx' to each side of the equation. 1.68ny + -1.5nx + -0.76y = 1.5nx + -1.5nx + -0.5x Reorder the terms: -1.5nx + 1.68ny + -0.76y = 1.5nx + -1.5nx + -0.5x Combine like terms: 1.5nx + -1.5nx = 0.0 -1.5nx + 1.68ny + -0.76y = 0.0 + -0.5x -1.5nx + 1.68ny + -0.76y = -0.5x Add '0.76y' to each side of the equation. -1.5nx + 1.68ny + -0.76y + 0.76y = -0.5x + 0.76y Combine like terms: -0.76y + 0.76y = 0.00 -1.5nx + 1.68ny + 0.00 = -0.5x + 0.76y -1.5nx + 1.68ny = -0.5x + 0.76y Reorder the terms: -1.5nx + 1.68ny + 0.5x + -0.76y = -0.5x + 0.5x + 0.76y + -0.76y Combine like terms: -0.5x + 0.5x = 0.0 -1.5nx + 1.68ny + 0.5x + -0.76y = 0.0 + 0.76y + -0.76y -1.5nx + 1.68ny + 0.5x + -0.76y = 0.76y + -0.76y Combine like terms: 0.76y + -0.76y = 0.00 -1.5nx + 1.68ny + 0.5x + -0.76y = 0.00 The solution to this equation could not be determined.
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