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Simplifying y[n] = 0.2x[n] + -0.8y[n + -1] + -0.15y[n + -2] Multiply y * n ny = 0.2x[n] + -0.8y[n + -1] + -0.15y[n + -2] Multiply x * n ny = 0.2nx + -0.8y[n + -1] + -0.15y[n + -2] Reorder the terms: ny = 0.2nx + -0.8y[-1 + n] + -0.15y[n + -2] ny = 0.2nx + [-1 * -0.8y + n * -0.8y] + -0.15y[n + -2] Reorder the terms: ny = 0.2nx + [-0.8ny + 0.8y] + -0.15y[n + -2] ny = 0.2nx + [-0.8ny + 0.8y] + -0.15y[n + -2] Reorder the terms: ny = 0.2nx + -0.8ny + 0.8y + -0.15y[-2 + n] ny = 0.2nx + -0.8ny + 0.8y + [-2 * -0.15y + n * -0.15y] Reorder the terms: ny = 0.2nx + -0.8ny + 0.8y + [-0.15ny + 0.3y] ny = 0.2nx + -0.8ny + 0.8y + [-0.15ny + 0.3y] Reorder the terms: ny = 0.2nx + -0.8ny + -0.15ny + 0.8y + 0.3y Combine like terms: -0.8ny + -0.15ny = -0.95ny ny = 0.2nx + -0.95ny + 0.8y + 0.3y Combine like terms: 0.8y + 0.3y = 1.1y ny = 0.2nx + -0.95ny + 1.1y Solving ny = 0.2nx + -0.95ny + 1.1y Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2nx' to each side of the equation. -0.2nx + ny = 0.2nx + -0.95ny + -0.2nx + 1.1y Reorder the terms: -0.2nx + ny = 0.2nx + -0.2nx + -0.95ny + 1.1y Combine like terms: 0.2nx + -0.2nx = 0.0 -0.2nx + ny = 0.0 + -0.95ny + 1.1y -0.2nx + ny = -0.95ny + 1.1y Add '0.95ny' to each side of the equation. -0.2nx + ny + 0.95ny = -0.95ny + 0.95ny + 1.1y Combine like terms: ny + 0.95ny = 1.95ny -0.2nx + 1.95ny = -0.95ny + 0.95ny + 1.1y Combine like terms: -0.95ny + 0.95ny = 0.00 -0.2nx + 1.95ny = 0.00 + 1.1y -0.2nx + 1.95ny = 1.1y Combine like terms: 1.1y + -1.1y = 0.0 -0.2nx + 1.95ny + -1.1y = 0.0 The solution to this equation could not be determined.
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