A boolean constraint satisfaction problem, CSP, is given by a large number of constraints each in a constant number of variables.  We are interested in the computational problem of given a set of constrains to
find the assignment that satisfies the largest number of constraints. 
Most problems of this type are NP-hard and the most famous example is  Max-Sat, given a set of clauses to satisfy the maximal number of clauses. Another interesting example is the case when the constraints are linear
equations over the finite field with two elements.  This problem is here called Max-Lin-2. Given that these problems are NP-hard and we are interested in polynomial time algorithms, we turn to analyzing heuristics.

A heuristic is a C-approximation if it on every instance finds an assignment that satisfies at most a factor C fewer constraints as compared with the optimal assignment.  For an instance of Max-Lin-2 it is easy to see that a random assignment satisfies half the constraints and it is not hard to turn this observation into an efficient (even deterministic) 2-approximation algorithm.  We prove that this is the best possible performance by proving the for any epsilon>0 it is NP-hard to 2-epsilon-approximate Max-Lin-2. As a consequence we prove that 8/7 is the best possible constant for Max-3Sat.