SOLUTION: Find all solutions in positive integers for x an y in which both x and y are less than 20 and 5x - 3y = 31. How would you do this using the diophantine equations?

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Question 618737: Find all solutions in positive integers for x an y in which both x and y are less than 20 and 5x - 3y = 31.
How would you do this using the diophantine equations?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Find all solutions in positive integers for x an y in which both x and y are less than 20:

5x - 3y = 31.

Diophantine Equation 

x = xo + pt

y = yo - qt

By trial and error (8,3) is one solution

x = 8 + pt

y = 3 - qt

As GCD of 5 and 3  is 1, therefore:

x = 8 + -3t

y = 3 - 5t



x = 8 -3t

y = 3 - 5t

t	x	y

0	8	3

-1	11	8

-2	14	13

-3	17	18