OE

Suppose x = 1 and y = –1. Then | x| + |y| = |1| + |–1| = 1 + 1 = 2, and x + y = 1 + (–1) = 0. Hence, x = 1 and y = –1 is a solution of the system of equations, and here x is greater than y.

Now, suppose x = –1 and y = 1. Then |x| + |y| = |–1| + |1| = 1 + 1 = 2, and x + y = –1 + 1 = 0. Hence, x = – 1 and y = 1 is another solution of the system of equations, and here x is less than y.

Thus, we have a double case, and the answer is (D).

Lets take the first equation |x|+|y| = 2 . so there is
Case 1 : x+y = 2 {(1,1),(0,2),(2,0)}
case 2 : -x+y = 2 {(-2,0)}
case 3 : {(5,3),(3,1),(6,4)}
case 4 : {(-1,-1)}
hence there is no specified relation , none of them have a pattern . undetermined relationship.