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Simplifying y(n) + y(n + -1) + 0.5y(n + -2) = x(n) + -1x(n + -1) Multiply y * n ny + y(n + -1) + 0.5y(n + -2) = x(n) + -1x(n + -1) Reorder the terms: ny + y(-1 + n) + 0.5y(n + -2) = x(n) + -1x(n + -1) ny + (-1 * y + n * y) + 0.5y(n + -2) = x(n) + -1x(n + -1) Reorder the terms: ny + (ny + -1y) + 0.5y(n + -2) = x(n) + -1x(n + -1) ny + (ny + -1y) + 0.5y(n + -2) = x(n) + -1x(n + -1) Reorder the terms: ny + ny + -1y + 0.5y(-2 + n) = x(n) + -1x(n + -1) ny + ny + -1y + (-2 * 0.5y + n * 0.5y) = x(n) + -1x(n + -1) Reorder the terms: ny + ny + -1y + (0.5ny + -1y) = x(n) + -1x(n + -1) ny + ny + -1y + (0.5ny + -1y) = x(n) + -1x(n + -1) Reorder the terms: ny + ny + 0.5ny + -1y + -1y = x(n) + -1x(n + -1) Combine like terms: ny + ny = 2ny 2ny + 0.5ny + -1y + -1y = x(n) + -1x(n + -1) Combine like terms: 2ny + 0.5ny = 2.5ny 2.5ny + -1y + -1y = x(n) + -1x(n + -1) Combine like terms: -1y + -1y = -2y 2.5ny + -2y = x(n) + -1x(n + -1) Multiply x * n 2.5ny + -2y = nx + -1x(n + -1) Reorder the terms: 2.5ny + -2y = nx + -1x(-1 + n) 2.5ny + -2y = nx + (-1 * -1x + n * -1x) Reorder the terms: 2.5ny + -2y = nx + (-1nx + 1x) 2.5ny + -2y = nx + (-1nx + 1x) Combine like terms: nx + -1nx = 0 2.5ny + -2y = 0 + 1x 2.5ny + -2y = 1x Solving 2.5ny + -2y = 1x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2y' to each side of the equation. 2.5ny + -2y + 2y = 1x + 2y Combine like terms: -2y + 2y = 0 2.5ny + 0 = 1x + 2y 2.5ny = 1x + 2y Divide each side by '2.5y'. n = 0.4xy-1 + 0.8 Simplifying n = 0.4xy-1 + 0.8 Reorder the terms: n = 0.8 + 0.4xy-1
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