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If $x + y = 10$ and $x^2 - y^2 = 40$, what is the value of $2x + 3y$?

 May 28, 2020
 #1
avatar+912 
+1

x is larger than y.

 

thus xy pairs are

 

6,4

7,3

8,2

9,1

10,0

 

So

 

36 - 16 = 20

49 - 9 = 40.

 

x = 7, y=3

 

You can take it from here.

 

If you don't understand anything feel free to ask.

 

Also fix your latex in the future.

 

There's a latex buttonnext to "image"

 May 28, 2020
 #2
avatar+30322 
+1

Can also do this as follows:

 

x + y = 10     (1)

 

x2 - y2 = 40  This can be written as  (x+y)(x-y) = 40.  Use (1)  to get  10*(x - y) = 40 or

 

x - y = 4      (2)

 

Add (1) and (2):  2x = 14,  so  x = 7  

Put this in (1) to get  7 + y = 10   or   y = 3

 May 28, 2020

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