Data Sufficiency

If |a-b|=c, then we can have either $$a-b=c\ \ OR\ \ a-b=-c$$ because of the properties of absolute values. For the statements to be sufficient, we need to find only one possible value for a. So unless we get a single value for a with BOTH equations, the statements are insufficient to solve.

You've already worked through why the statements individually aren't sufficient to solve, so we'll look at them together:

If b = 2 and c = 7, we can have either $$a-2=7\ \ OR\ \ a-2=-7$$
Solving for a in both equations gives $$a=9\ \ OR\ \ a=-5$$

This means that there are two possible values for a: 9 and -5. Insufficient.