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