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Simplifying y[n] = 0.25y[n + -1] + 3x[n] + -1x[n + -1] Multiply y * n ny = 0.25y[n + -1] + 3x[n] + -1x[n + -1] Reorder the terms: ny = 0.25y[-1 + n] + 3x[n] + -1x[n + -1] ny = [-1 * 0.25y + n * 0.25y] + 3x[n] + -1x[n + -1] Reorder the terms: ny = [0.25ny + -0.25y] + 3x[n] + -1x[n + -1] ny = [0.25ny + -0.25y] + 3x[n] + -1x[n + -1] Multiply x * n ny = 0.25ny + -0.25y + 3nx + -1x[n + -1] Reorder the terms: ny = 0.25ny + -0.25y + 3nx + -1x[-1 + n] ny = 0.25ny + -0.25y + 3nx + [-1 * -1x + n * -1x] Reorder the terms: ny = 0.25ny + -0.25y + 3nx + [-1nx + 1x] ny = 0.25ny + -0.25y + 3nx + [-1nx + 1x] Reorder the terms: ny = 3nx + -1nx + 0.25ny + 1x + -0.25y Combine like terms: 3nx + -1nx = 2nx ny = 2nx + 0.25ny + 1x + -0.25y Solving ny = 2nx + 0.25ny + 1x + -0.25y Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2nx' to each side of the equation. -2nx + ny = 2nx + 0.25ny + 1x + -2nx + -0.25y Reorder the terms: -2nx + ny = 2nx + -2nx + 0.25ny + 1x + -0.25y Combine like terms: 2nx + -2nx = 0 -2nx + ny = 0 + 0.25ny + 1x + -0.25y -2nx + ny = 0.25ny + 1x + -0.25y Add '-0.25ny' to each side of the equation. -2nx + ny + -0.25ny = 0.25ny + 1x + -0.25ny + -0.25y Combine like terms: ny + -0.25ny = 0.75ny -2nx + 0.75ny = 0.25ny + 1x + -0.25ny + -0.25y Reorder the terms: -2nx + 0.75ny = 0.25ny + -0.25ny + 1x + -0.25y Combine like terms: 0.25ny + -0.25ny = 0.00 -2nx + 0.75ny = 0.00 + 1x + -0.25y -2nx + 0.75ny = 1x + -0.25y Reorder the terms: -2nx + 0.75ny + -1x + 0.25y = 1x + -1x + -0.25y + 0.25y Combine like terms: 1x + -1x = 0 -2nx + 0.75ny + -1x + 0.25y = 0 + -0.25y + 0.25y -2nx + 0.75ny + -1x + 0.25y = -0.25y + 0.25y Combine like terms: -0.25y + 0.25y = 0.00 -2nx + 0.75ny + -1x + 0.25y = 0.00 The solution to this equation could not be determined.
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