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What is the ordered pair of integers $(x,y)$ for which $12x + 21y = 15$ and $21x + 12y = 51$?

 Apr 12, 2018
 #1
avatar+638 
+2

This is a system of equations problem.  

 

To easiest way to solve this is first add both equations. 

 

12x + 21y + 21x + 12y = 51 + 15

 

So 33 y + 33x = 66 

 

x + y = 2 

 

We can use x = 2 - y and plug this in to equation #1.

 

12 ( 2 - y ) + 21y = 15 

 

24 - 12y + 21y = 15

 

y = -1 

x = 3 

 

The ordered pair you are looking for is (3, -1)

 Apr 12, 2018
 #2
avatar+606 
+1

Thank you!

gueesstt  Apr 12, 2018

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