Astudent government organization is selling christmas trees as a fundraiser. on friday, they sold 5 noble fir trees and 3 douglas fir trees for a total of $420. on saturday, 12 noble fir trees and 9 douglas fir trees were sold for a total of $1,080. what is the cost per tree for each type?

So you must set this up as a system of equations
n= noble fir trees
d= douglas fir trees
5n + 3d = $420
12n + 9d = $1,080 
To get a positive output you have to multiply the second equation by 3 to be able to be divisable to one another 
36n + 18d = 3,240
now divide the equation by 18 
2n + d = 180
-2n        -2n
d = 180 - 2n
Now put that equation in the first as d ^^^
5n + 3(180 -2n) = 420
5n + 540- 6n = 420 
      - 540         -540 
1n = 120 
n = 120 
Now put n into the second equation( none changed one) to find d 
12(120) + 9d = 3240 
1440 + 9d = 3240 
-1440        -1440
9d = 1800
÷9    ÷9
d= 200
so the noble is $ 120 
and the douglas is $200

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !