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