I have an equation in the form ax + by = 1 where a and b are known integers. I need to come up with a method to find the possible solutions for x and y, but the trick is that x and y must also be integers. So the usual algebraic linear graph doesn't work very well.

Can anybody suggest a method to do this? Is there an algebraic way? I'm also open to using a TI-89 or Wolfram Alpha, if you know how to program these devices to accomplish this.

Thank you!