Which one of the following statements is correct for the given system?

For Linear System :

System must satisfy additivity and homogeneity.

for input x₁(n) : 

for input x₂(n)

for input x(n) = x₁(n) + x₂(n)

y(n)  y₁(n)+y₂(n) 

Hence Not Linear.

The present output depends on present and past values of input hence causal system.

Time Invariance :

For delayed input x(n-t)

For delayed output y (n-t)

y(n-t) = y₁(n)

Hence Time/Shift-Invariant System.