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Simplifying y(n) = 0.5y(n + -1) + -0.06y(n + -2) + x(n) + -0.5x(n + -2) Multiply y * n ny = 0.5y(n + -1) + -0.06y(n + -2) + x(n) + -0.5x(n + -2) Reorder the terms: ny = 0.5y(-1 + n) + -0.06y(n + -2) + x(n) + -0.5x(n + -2) ny = (-1 * 0.5y + n * 0.5y) + -0.06y(n + -2) + x(n) + -0.5x(n + -2) Reorder the terms: ny = (0.5ny + -0.5y) + -0.06y(n + -2) + x(n) + -0.5x(n + -2) ny = (0.5ny + -0.5y) + -0.06y(n + -2) + x(n) + -0.5x(n + -2) Reorder the terms: ny = 0.5ny + -0.5y + -0.06y(-2 + n) + x(n) + -0.5x(n + -2) ny = 0.5ny + -0.5y + (-2 * -0.06y + n * -0.06y) + x(n) + -0.5x(n + -2) Reorder the terms: ny = 0.5ny + -0.5y + (-0.06ny + 0.12y) + x(n) + -0.5x(n + -2) ny = 0.5ny + -0.5y + (-0.06ny + 0.12y) + x(n) + -0.5x(n + -2) Multiply x * n ny = 0.5ny + -0.5y + -0.06ny + 0.12y + nx + -0.5x(n + -2) Reorder the terms: ny = 0.5ny + -0.5y + -0.06ny + 0.12y + nx + -0.5x(-2 + n) ny = 0.5ny + -0.5y + -0.06ny + 0.12y + nx + (-2 * -0.5x + n * -0.5x) Reorder the terms: ny = 0.5ny + -0.5y + -0.06ny + 0.12y + nx + (-0.5nx + 1x) ny = 0.5ny + -0.5y + -0.06ny + 0.12y + nx + (-0.5nx + 1x) Reorder the terms: ny = nx + -0.5nx + 0.5ny + -0.06ny + 1x + -0.5y + 0.12y Combine like terms: nx + -0.5nx = 0.5nx ny = 0.5nx + 0.5ny + -0.06ny + 1x + -0.5y + 0.12y Combine like terms: 0.5ny + -0.06ny = 0.44ny ny = 0.5nx + 0.44ny + 1x + -0.5y + 0.12y Combine like terms: -0.5y + 0.12y = -0.38y ny = 0.5nx + 0.44ny + 1x + -0.38y Solving ny = 0.5nx + 0.44ny + 1x + -0.38y Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5nx' to each side of the equation. -0.5nx + ny = 0.5nx + 0.44ny + 1x + -0.5nx + -0.38y Reorder the terms: -0.5nx + ny = 0.5nx + -0.5nx + 0.44ny + 1x + -0.38y Combine like terms: 0.5nx + -0.5nx = 0.0 -0.5nx + ny = 0.0 + 0.44ny + 1x + -0.38y -0.5nx + ny = 0.44ny + 1x + -0.38y Add '-0.44ny' to each side of the equation. -0.5nx + ny + -0.44ny = 0.44ny + 1x + -0.44ny + -0.38y Combine like terms: ny + -0.44ny = 0.56ny -0.5nx + 0.56ny = 0.44ny + 1x + -0.44ny + -0.38y Reorder the terms: -0.5nx + 0.56ny = 0.44ny + -0.44ny + 1x + -0.38y Combine like terms: 0.44ny + -0.44ny = 0.00 -0.5nx + 0.56ny = 0.00 + 1x + -0.38y -0.5nx + 0.56ny = 1x + -0.38y Reorder the terms: -0.5nx + 0.56ny + -1x + 0.38y = 1x + -1x + -0.38y + 0.38y Combine like terms: 1x + -1x = 0 -0.5nx + 0.56ny + -1x + 0.38y = 0 + -0.38y + 0.38y -0.5nx + 0.56ny + -1x + 0.38y = -0.38y + 0.38y Combine like terms: -0.38y + 0.38y = 0.00 -0.5nx + 0.56ny + -1x + 0.38y = 0.00 The solution to this equation could not be determined.
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