An algebra problem by Cristiano Dilip

Matthew Shelborn frequently has to travel for his company, which gives him a chance to meet many people from all parts of the USA. In April, Matthew flew to five different US cities on business and he flew a different airline each time. During each trip he chatted with the person next to him, and no two people he talked to were in the same profession.

From the information, can you determine his destination ?

1. Three consecutive flights were, in order from first to last, the flight Matthew took with WTA Airways, the flight where he sat next to the teacher, and the flight he took to Atlanta.

2. Matthew sat beside the sports coach on a flight some time earlier in the month than the one he took to Seattle.

3. The week he flew Air Express was some time earlier in the month than the trip to Boston, which was some time earlier in the month than the trip where he sat next to the ballet dancer.

4. It wasn't on the trip to San Diego where Matthew sat next to the doctor.

5. Matthew didn't fly Skyways on his trip to Seattle, and he didn't fly WTA Airways on the trip where he sat next to the sports coach.

6. Atlanta was not Matthew's destination on the trip where he made the acquaintance of the ballet dancer.

7. The Fly America flight was exactly two weeks before the flight where Matthew passed the time chatting with the attorney.