Does s = 5 - t ?

The question is:
Is s + t = 5?

Statement (1) t = 17 - 4s
4s + t = 17 ........(I)
This statement alone is not enough. You don't know what s + t is.

Statement (2) s = 8 - 4t
s + 4t = 8 ...........(II)
Again, this statement alone is not enough. You don't know what s + t is.

Using both, you can solve the equations simultaneously. Add (I) and (II)
4s + t = 17
s + 4t = 8
--------------
5s + 5t = 25
s + t = 5

From both the statements, you get that s + t is actually equal to 5. Your answer is 'Yes'.
So (C)

If you had obtained s + t = something other than 5 using both the statements, you would still have obtained a decisive 'No' to the question. Hence your answer would still have been (C)