Question 1209224
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Answer: <font color=red>243</font>


Work Shown


(9^x)/(27^y)
= ((3^2)^x)/((3^3)^y)
= (3^(2x))/(3^(3y))
= 3^(2x-3y)
= 3^(5)
= <font color=red>243</font>


We conclude that (9^x)/(27^y) = <font color=red>243</font> when 2x-3y = 5.


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Another approach.


Pick any point on the line 2x-3y = 5. 
Let's say we pick the point (x,y) = (4,1). 
You can determine this point by looking at the graph, or do a bit of trial-and-error. 


Note that 2x-3y = 2*4-3*1 = 8-3 = 5 which confirms (4,1) is on this line. 
This ordered pair makes 2x-3y = 5 true.


(9^x)/(27^y)
= (9^4)/(27^1)
= (6561)/(27)
= <font color=red>243</font>
We arrive at the same answer.
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