Amath contest requires that participants complete all 12 problems on the contest exam. each participant receives 5 points for each correctly solved problem and loses 3 points for each incorrect or omitted answer. if i received a score of 36, how many problems did i solve correctly?

You got 9 right, because 5x -3y = 36
For you to lose points, having answered all of thee questions, to the point of which you were given 36 out of 60 possible points tells that you must have gotten over half right for points to have been taken away, and the only factors that satisfy the equation with those restrictions would determine that x must equal 9, making the amount you got right worth 45 points, but with y equal to 3, 9 points were taken away from that score, making it 36. This can also be displayed on a x versus y graph.