SOLUTION: Find the value of x + y where x and y are positive integers that satisfy: 13x + 19y = 212. I know you could try plugging in numbers until you get the right pair, but I know th

Question 618735: Find the value of x + y where x and y are positive integers that
satisfy: 13x + 19y = 212.
I know you could try plugging in numbers until you get the right
pair, but I know there has to be a way to do this using the
Diophantine equation method.

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

 

Hi,

Find the value of  where x and y are positive integers that 

satisfy: 13x + 19y = 212.

x = xo + pt

y = yo - qt

by trial and error find(9,5) to be a solution

x = 9 + pt

y = 5 - qt

As GCD of 13 and 19 is 1, therefore:

x = 9 + 19t

y = 5 - 13t

(x + y) = 6t +14 

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