Proving System is Time Invariant (T.I.) or Not

[SpaceDomain]

Homework Statement

Prove that the system is either T.I. or is not T.I.

Homework Equations

y(n) = x(n)*h(n)

x(n) is the input signal
y(n) is the output signal
h(n) is the system

The Attempt at a Solution

Inputing x(n-n0) into the system I get out:
as the output x(n-n0)*h(n)

Since y(n-n0) = x(n-n0)*h(n-n0) != x(n-n0)*h(n) the system is not T.I.

I think I am doing this wrong.

 

[reddvoid]

Inputing x(n-n0) into the system I get out:
as the output x(n-n0)*h(n)

how can you get this output for x(n-n0) input ?

 

[SpaceDomain]

how can you get this output for x(n-n0) input ?

So should it be that an input of x(n-n0) results in x(n-n0)*h(n-n0)?

 

[reddvoid]

no,
you are telling
x(n) is input of the system
y(n) is out put of the system
h(n) is its transfer function

in-order to check whether the system is TV or TIV we need the relation between input and output.
for example if you tell y(t) output =sin times input x(t)
then we can check whether its TV or TIV
or we need the impulse response function h(t) to decide whether it is TV or TIV

you have not given anything
for every system y(t) is equal to x(t)*h(t)
but their response depends on the function h(t) which is different for different systems

P.S.
I hope you understood