What is the cost for a member to play a round of golf, what is the cost for a noember?

Let m and n represent the costs for members and non-members, respectively.

m + 6n = 255
2m +3n = 150

You can eliminate n by subtracting the first equation from twice the second.
2(2m +3n) -(m +6n) = 2(150) -(255)
3m = 45 . . . . . . . . . . . . collect terms
m = 15 . . . . . . . . . . . . .. divide by 3

Then
15 +6n = 255 . . . . . substituting for m in the first equation
6n = 240 . . . . . . . .. subtract 15
n = 40 . . . . . . . . . . . divide by 6

The cost per member is $15.
The cost per non-member is $40.