The following is asked:
What is the value of x?

1) -(x+y) = x-y
2) x+y = 2

I first look to #2 as the easy statement. I rebalance the equation so that x= 2-y. Why is this not a sufficient value for x? The question does not ask for a numeric value of x, but simple a value. Even if I haven't solved for y, doesn't 2-y represent a value?

The question implies the numrical value indeed!!!

Any time the test asks for a value, it is referring to a numerical value. To be sufficient, a statement has to provide a definitive numerical value (if it asked for a value - some questions are worded as yes/no questions instead).