H + C = 650     (1)    ("a combined total of 650 hamburgers and cheeseburgers")
C = H - 50      (2)    ("There were 50 fewer cheeseburgers sold than hamburgers.")


Substitute C = H - 50  into (2),  based on (1).


You will get


H + (H-50) = 650  ====>  2H - 50 = 650  ====>  2H = 650+50 = 700  ====>  H = 350 hamburgers.


Answer.  350 hamburgers and 300 cheeseburgers.