IMO 1967 LL BUL6

Solve the system

IMO 1967 LL BUL6

Origin: BUL

Problem

Solve the system |x + y| + |1 −x| = 6, |x + y + 1| + |1 −y| = 4.

Solution

The given system has two solutions: (−2, −1) and (−14/3, 13/3).