Solve the Diophantine equation 7x11y321SolutionDiophantine e

Solve the Diophantine equation 7x+11y=321.

Diophantine equation 7x+11y=321.

This is a linear equation in x,y.

By trial and error we see x =1,2,3,4 do not give integer y

x =5 gives 11y = 321-35 = 286

Since 286 is divisible by 11, y = 26

Hence (5,26) is one solution.

Next will be 5+11 =16 for x

x =16 then 112+11y = 321

11y = 209

y = 19

Thus solutions are

(5,26), (11,19) (27,12), (38, 5)

Only 4 solutions are possible in positive integers.