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Simplifying y(n) = x(n) + 5x(n + -1) + 4x(n + -2) + -4y(n + -1) + -4y(n + -2) Multiply y * n ny = x(n) + 5x(n + -1) + 4x(n + -2) + -4y(n + -1) + -4y(n + -2) Multiply x * n ny = nx + 5x(n + -1) + 4x(n + -2) + -4y(n + -1) + -4y(n + -2) Reorder the terms: ny = nx + 5x(-1 + n) + 4x(n + -2) + -4y(n + -1) + -4y(n + -2) ny = nx + (-1 * 5x + n * 5x) + 4x(n + -2) + -4y(n + -1) + -4y(n + -2) Reorder the terms: ny = nx + (5nx + -5x) + 4x(n + -2) + -4y(n + -1) + -4y(n + -2) ny = nx + (5nx + -5x) + 4x(n + -2) + -4y(n + -1) + -4y(n + -2) Reorder the terms: ny = nx + 5nx + -5x + 4x(-2 + n) + -4y(n + -1) + -4y(n + -2) ny = nx + 5nx + -5x + (-2 * 4x + n * 4x) + -4y(n + -1) + -4y(n + -2) Reorder the terms: ny = nx + 5nx + -5x + (4nx + -8x) + -4y(n + -1) + -4y(n + -2) ny = nx + 5nx + -5x + (4nx + -8x) + -4y(n + -1) + -4y(n + -2) Reorder the terms: ny = nx + 5nx + -5x + 4nx + -8x + -4y(-1 + n) + -4y(n + -2) ny = nx + 5nx + -5x + 4nx + -8x + (-1 * -4y + n * -4y) + -4y(n + -2) Reorder the terms: ny = nx + 5nx + -5x + 4nx + -8x + (-4ny + 4y) + -4y(n + -2) ny = nx + 5nx + -5x + 4nx + -8x + (-4ny + 4y) + -4y(n + -2) Reorder the terms: ny = nx + 5nx + -5x + 4nx + -8x + -4ny + 4y + -4y(-2 + n) ny = nx + 5nx + -5x + 4nx + -8x + -4ny + 4y + (-2 * -4y + n * -4y) Reorder the terms: ny = nx + 5nx + -5x + 4nx + -8x + -4ny + 4y + (-4ny + 8y) ny = nx + 5nx + -5x + 4nx + -8x + -4ny + 4y + (-4ny + 8y) Reorder the terms: ny = nx + 5nx + 4nx + -4ny + -4ny + -5x + -8x + 4y + 8y Combine like terms: nx + 5nx = 6nx ny = 6nx + 4nx + -4ny + -4ny + -5x + -8x + 4y + 8y Combine like terms: 6nx + 4nx = 10nx ny = 10nx + -4ny + -4ny + -5x + -8x + 4y + 8y Combine like terms: -4ny + -4ny = -8ny ny = 10nx + -8ny + -5x + -8x + 4y + 8y Combine like terms: -5x + -8x = -13x ny = 10nx + -8ny + -13x + 4y + 8y Combine like terms: 4y + 8y = 12y ny = 10nx + -8ny + -13x + 12y Solving ny = 10nx + -8ny + -13x + 12y Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10nx' to each side of the equation. -10nx + ny = 10nx + -8ny + -13x + -10nx + 12y Reorder the terms: -10nx + ny = 10nx + -10nx + -8ny + -13x + 12y Combine like terms: 10nx + -10nx = 0 -10nx + ny = 0 + -8ny + -13x + 12y -10nx + ny = -8ny + -13x + 12y Add '8ny' to each side of the equation. -10nx + ny + 8ny = -8ny + -13x + 8ny + 12y Combine like terms: ny + 8ny = 9ny -10nx + 9ny = -8ny + -13x + 8ny + 12y Reorder the terms: -10nx + 9ny = -8ny + 8ny + -13x + 12y Combine like terms: -8ny + 8ny = 0 -10nx + 9ny = 0 + -13x + 12y -10nx + 9ny = -13x + 12y Reorder the terms: -10nx + 9ny + 13x + -12y = -13x + 13x + 12y + -12y Combine like terms: -13x + 13x = 0 -10nx + 9ny + 13x + -12y = 0 + 12y + -12y -10nx + 9ny + 13x + -12y = 12y + -12y Combine like terms: 12y + -12y = 0 -10nx + 9ny + 13x + -12y = 0 The solution to this equation could not be determined.
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