To solve this problem, we need to analyze the given information and use logical deductions to find the scores for the last two rounds.
Let's first calculate the total score for the first 8 rounds:
+5 - 2 + 3 - 1 - 3 + 6 + 2 - 7 = 3 strokes over par
Since the golfer played 10 rounds in total and the cumulative score for all 10 rounds is even par, we know that the remaining two rounds must cancel out the 3 strokes over par from the first 8 rounds.
Let's assume the score for the ninth round is x. Since the score for the last round is 7 more than the score on the next-to-last round, we can represent it as x + 7.
Now, let's set up the equation:
(x) + (x + 7) = -3
Simplifying the equation gives us:
2x + 7 = -3
2x = -10
x = -5
So, the score for the ninth round is -5, and the score for the last round is:
(-5) + 7 = +2
Therefore, the scores for the last two rounds are -5 and +2, respectively.