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Consider the following input $x(t)$ and output $y(t)$ pairs for two different systems.

- $x(t)=\sin (t), y(t)=\cos (t),$
- $x(t)=t+\sin (t), y(t)=2 t+\sin (t-1).$

Which of these systems could possibly be linear and time invariant? Choose the most appropriate answer from below.

- (i), but not (ii).
- (ii), but not (i).
- both (i) and (ii).
- neither (i) nor (ii).
- neither, but a system with $x(t)=\sin (2 t), y(t)=\sin (t) \cos (t) \operatorname{could~be.~}$