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Simplifying 2y[n] + y[n + -1] + -3y[n + -2] = x[n + 1] + 7x[n] Multiply y * n 2ny + y[n + -1] + -3y[n + -2] = x[n + 1] + 7x[n] Reorder the terms: 2ny + y[-1 + n] + -3y[n + -2] = x[n + 1] + 7x[n] 2ny + [-1 * y + n * y] + -3y[n + -2] = x[n + 1] + 7x[n] Reorder the terms: 2ny + [ny + -1y] + -3y[n + -2] = x[n + 1] + 7x[n] 2ny + [ny + -1y] + -3y[n + -2] = x[n + 1] + 7x[n] Reorder the terms: 2ny + ny + -1y + -3y[-2 + n] = x[n + 1] + 7x[n] 2ny + ny + -1y + [-2 * -3y + n * -3y] = x[n + 1] + 7x[n] Reorder the terms: 2ny + ny + -1y + [-3ny + 6y] = x[n + 1] + 7x[n] 2ny + ny + -1y + [-3ny + 6y] = x[n + 1] + 7x[n] Reorder the terms: 2ny + ny + -3ny + -1y + 6y = x[n + 1] + 7x[n] Combine like terms: 2ny + ny = 3ny 3ny + -3ny + -1y + 6y = x[n + 1] + 7x[n] Combine like terms: 3ny + -3ny = 0 0 + -1y + 6y = x[n + 1] + 7x[n] -1y + 6y = x[n + 1] + 7x[n] Combine like terms: -1y + 6y = 5y 5y = x[n + 1] + 7x[n] Reorder the terms: 5y = x[1 + n] + 7x[n] 5y = [1 * x + n * x] + 7x[n] Reorder the terms: 5y = [nx + 1x] + 7x[n] 5y = [nx + 1x] + 7x[n] Multiply x * n 5y = nx + 1x + 7nx Reorder the terms: 5y = nx + 7nx + 1x Combine like terms: nx + 7nx = 8nx 5y = 8nx + 1x Solving 5y = 8nx + 1x Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Divide each side by '5'. y = 1.6nx + 0.2x Simplifying y = 1.6nx + 0.2x
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