I'm looking for an algorithm to create a very simple (2 equations, 2 unknowns) linear system of equations that consists purely of integers. Specifically, a way to create a system of equations of integers and knowing that it can only be solved by integer answers, without actually solving it. a11x1+a12x2=b1 a21x1+a22x2=b2 where a11, a12, a21, a22, x1, x2, b1, b2 are all integers. The only thing I can think of is using a determinant which gives x1 = (a22b1-a12b2) / (a11a22-a12a21) x2 = (a11b2-a21b1) / (a11a22-a12a21) and that the numerator must be a multiple of the denominator. What do I do now? Am I even on the right path?