x + 4y = 9

x = 9 - 4y thus x is integer if y is integer

thus the solution of the equation are all pairs

(9 - 4t, t), where t is integer

for example let t =1 then 9 - 4t = 5

for the pair (5,1) we have 5 + 4*1 = 9 thus (5,1) is a solution.