CAT 2017 Quantitative Ability

|x + y| = | x - y|
⇒ (x+y)2=(x−y)2
⇒4xy=0
⇒ either x = 0 or y = 0

If x = 0 and y is any real number, we have infinite possible values of y as
|0 + y| = |0 - y| =>|y| =|- y|

Similarly, (x, 0) where x can be any real number also satisfies |x + 0| = |x - 0|
So, there are infinite number of solutions.