Since this question does not ask us to solve, we can look at the structure of the equations.
We need to first notice that the second equation in all the answer choices is identical to the one given.
Therefore, all of our energy should be directed at the top(first) equation so we will  compare the top equations in all 4 answers.
The correct answer will be a multiple of the top given equation:

Answer (1):   -2x – 2y = -6 almost looks like -2(x – y =3)
Answer (2):  -2x + 2y = 3 (if you multiply -2(x – y =3), the right hand side will have to be -6
Answer (3):  2x – 2y = 6 (this looks a LOT like x – y = 3!!!)
Answer (4): 3x + 3y = 9 almost looks like 3(x – y = 3) but not quite