Question 618737
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Hi,
Find all solutions in <u>positive integers</u> 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