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Simplifying y(n) = x(n) + 3x(n + -1) + 4x(n + -2) + -5y(n + -1) + -5y(n + -2) Multiply y * n ny = x(n) + 3x(n + -1) + 4x(n + -2) + -5y(n + -1) + -5y(n + -2) Multiply x * n ny = nx + 3x(n + -1) + 4x(n + -2) + -5y(n + -1) + -5y(n + -2) Reorder the terms: ny = nx + 3x(-1 + n) + 4x(n + -2) + -5y(n + -1) + -5y(n + -2) ny = nx + (-1 * 3x + n * 3x) + 4x(n + -2) + -5y(n + -1) + -5y(n + -2) Reorder the terms: ny = nx + (3nx + -3x) + 4x(n + -2) + -5y(n + -1) + -5y(n + -2) ny = nx + (3nx + -3x) + 4x(n + -2) + -5y(n + -1) + -5y(n + -2) Reorder the terms: ny = nx + 3nx + -3x + 4x(-2 + n) + -5y(n + -1) + -5y(n + -2) ny = nx + 3nx + -3x + (-2 * 4x + n * 4x) + -5y(n + -1) + -5y(n + -2) Reorder the terms: ny = nx + 3nx + -3x + (4nx + -8x) + -5y(n + -1) + -5y(n + -2) ny = nx + 3nx + -3x + (4nx + -8x) + -5y(n + -1) + -5y(n + -2) Reorder the terms: ny = nx + 3nx + -3x + 4nx + -8x + -5y(-1 + n) + -5y(n + -2) ny = nx + 3nx + -3x + 4nx + -8x + (-1 * -5y + n * -5y) + -5y(n + -2) Reorder the terms: ny = nx + 3nx + -3x + 4nx + -8x + (-5ny + 5y) + -5y(n + -2) ny = nx + 3nx + -3x + 4nx + -8x + (-5ny + 5y) + -5y(n + -2) Reorder the terms: ny = nx + 3nx + -3x + 4nx + -8x + -5ny + 5y + -5y(-2 + n) ny = nx + 3nx + -3x + 4nx + -8x + -5ny + 5y + (-2 * -5y + n * -5y) Reorder the terms: ny = nx + 3nx + -3x + 4nx + -8x + -5ny + 5y + (-5ny + 10y) ny = nx + 3nx + -3x + 4nx + -8x + -5ny + 5y + (-5ny + 10y) Reorder the terms: ny = nx + 3nx + 4nx + -5ny + -5ny + -3x + -8x + 5y + 10y Combine like terms: nx + 3nx = 4nx ny = 4nx + 4nx + -5ny + -5ny + -3x + -8x + 5y + 10y Combine like terms: 4nx + 4nx = 8nx ny = 8nx + -5ny + -5ny + -3x + -8x + 5y + 10y Combine like terms: -5ny + -5ny = -10ny ny = 8nx + -10ny + -3x + -8x + 5y + 10y Combine like terms: -3x + -8x = -11x ny = 8nx + -10ny + -11x + 5y + 10y Combine like terms: 5y + 10y = 15y ny = 8nx + -10ny + -11x + 15y Solving ny = 8nx + -10ny + -11x + 15y Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8nx' to each side of the equation. -8nx + ny = 8nx + -10ny + -11x + -8nx + 15y Reorder the terms: -8nx + ny = 8nx + -8nx + -10ny + -11x + 15y Combine like terms: 8nx + -8nx = 0 -8nx + ny = 0 + -10ny + -11x + 15y -8nx + ny = -10ny + -11x + 15y Add '10ny' to each side of the equation. -8nx + ny + 10ny = -10ny + -11x + 10ny + 15y Combine like terms: ny + 10ny = 11ny -8nx + 11ny = -10ny + -11x + 10ny + 15y Reorder the terms: -8nx + 11ny = -10ny + 10ny + -11x + 15y Combine like terms: -10ny + 10ny = 0 -8nx + 11ny = 0 + -11x + 15y -8nx + 11ny = -11x + 15y Reorder the terms: -8nx + 11ny + 11x + -15y = -11x + 11x + 15y + -15y Combine like terms: -11x + 11x = 0 -8nx + 11ny + 11x + -15y = 0 + 15y + -15y -8nx + 11ny + 11x + -15y = 15y + -15y Combine like terms: 15y + -15y = 0 -8nx + 11ny + 11x + -15y = 0 The solution to this equation could not be determined.
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