Question

5x + 7y = 19

I'm having problems finding three solutions, So far I found (1,2). Do I need to just keep on substituting numbers till I get a correct one? It's taking me ages, any faster methods?

Answer 1

Do you mean integer solutions?

Answer 2

(-6,7) (1,2) and (8,-3)

Answer 3

I take it you just kept on substituting numbers till you got a valid solution huh :/

Damn was hoping for there to be some other way to do this faster, thanks for the help.

Answer 4

yeah well if u got more just lemme know

Answer 5

if you know one integer solution for Ax+By = C, call it (x1, y1), then you can find any integer solution using the equations

x = x1 + B*k
y = x2 - A*k

for any integer k


For example, if k = 2, then

x = x1 + B*k
y = x2 - A*k


x = 1 + 7*k
y = 2 - 5*k


x = 1 + 7*2
y = 2 - 5*2


x = 15
y = -8


So (15,-8) is another integer solution