Question 618734
Step one - use trial and error to find one solution for x,y.<P>
In this case, use x=162 and y=-7:  (13*162+14(-7) = 2106 - 98 = 2008)<P>
The general solution is x=x(0) + pt and y = y(0) - qt where x(0) and y(0) are the values found from trial and error, p = b (coefficient of y) / GCD (a,b) and q = a (coefficient of x) / GCD(a,b) and t is an integer.<P>
The GCD of a and b is 1.  So p = 14/1 = 14 and q = 13/1 = 13.<P>
So the solution in this case is x = 162+14t and y = -7 - 13t
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