Find a solution to the equation 512x 200y 8 for integers x

Find a solution to the equation

512x + 200y = 8

for integers x,y

Now let c be any integer . Give a solution to 512x+200y = 8c

Solution

512x +200y = 8

x = 0

200y = 8

y = 8/200

y = 1/25

x = 1

512 + 200y = 8

200y = 8 - 512

200y = -504

y = -504/200

y = -2.52

512x + 200y = 8c

x = 1

200y = 8c-512

y = 8c-512/200