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