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Simplifying y[n + 2] + 0.5[n + 1] + 0.25[n] = x[n + 1] + -1x[n] Reorder the terms: y[2 + n] + 0.5[n + 1] + 0.25[n] = x[n + 1] + -1x[n] [2 * y + n * y] + 0.5[n + 1] + 0.25[n] = x[n + 1] + -1x[n] Reorder the terms: [ny + 2y] + 0.5[n + 1] + 0.25[n] = x[n + 1] + -1x[n] [ny + 2y] + 0.5[n + 1] + 0.25[n] = x[n + 1] + -1x[n] Reorder the terms: ny + 2y + 0.5[1 + n] + 0.25[n] = x[n + 1] + -1x[n] ny + 2y + [1 * 0.5 + n * 0.5] + 0.25[n] = x[n + 1] + -1x[n] ny + 2y + [0.5 + 0.5n] + 0.25[n] = x[n + 1] + -1x[n] Reorder the terms: 0.5 + 0.5n + 0.25n + ny + 2y = x[n + 1] + -1x[n] Combine like terms: 0.5n + 0.25n = 0.75n 0.5 + 0.75n + ny + 2y = x[n + 1] + -1x[n] Reorder the terms: 0.5 + 0.75n + ny + 2y = x[1 + n] + -1x[n] 0.5 + 0.75n + ny + 2y = [1 * x + n * x] + -1x[n] Reorder the terms: 0.5 + 0.75n + ny + 2y = [nx + 1x] + -1x[n] 0.5 + 0.75n + ny + 2y = [nx + 1x] + -1x[n] Multiply x * n 0.5 + 0.75n + ny + 2y = nx + 1x + -1nx Reorder the terms: 0.5 + 0.75n + ny + 2y = nx + -1nx + 1x Combine like terms: nx + -1nx = 0 0.5 + 0.75n + ny + 2y = 0 + 1x 0.5 + 0.75n + ny + 2y = 1x Solving 0.5 + 0.75n + ny + 2y = 1x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + 0.75n + ny + -0.5 + 2y = -0.5 + 1x Reorder the terms: 0.5 + -0.5 + 0.75n + ny + 2y = -0.5 + 1x Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.75n + ny + 2y = -0.5 + 1x 0.75n + ny + 2y = -0.5 + 1x Add '-2y' to each side of the equation. 0.75n + ny + 2y + -2y = -0.5 + 1x + -2y Combine like terms: 2y + -2y = 0 0.75n + ny + 0 = -0.5 + 1x + -2y 0.75n + ny = -0.5 + 1x + -2y Reorder the terms: 0.5 + 0.75n + ny + -1x + 2y = -0.5 + 1x + -2y + 0.5 + -1x + 2y Reorder the terms: 0.5 + 0.75n + ny + -1x + 2y = -0.5 + 0.5 + 1x + -1x + -2y + 2y Combine like terms: -0.5 + 0.5 = 0.0 0.5 + 0.75n + ny + -1x + 2y = 0.0 + 1x + -1x + -2y + 2y 0.5 + 0.75n + ny + -1x + 2y = 1x + -1x + -2y + 2y Combine like terms: 1x + -1x = 0 0.5 + 0.75n + ny + -1x + 2y = 0 + -2y + 2y 0.5 + 0.75n + ny + -1x + 2y = -2y + 2y Combine like terms: -2y + 2y = 0 0.5 + 0.75n + ny + -1x + 2y = 0 The solution to this equation could not be determined.
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