1. The problem statement, all variables and given/known data Let S be the set of all lines with equation y = mx+b for which m+b = 36. For how many of the elements of S are both the x- and y-intercepts integers? 2. Relevant equations y = mx+b for which m+b = 36 3. The attempt at a solution I'm just not wrapping my mind around the steps in the solution here: Denote by (a,0); (0, b) correspondingly x-intercept and y-intercept of a line. Adding the equalities given in the problem and simplifying the result, we will come to the equation of the set of the lines y = (m-1)x+36 From that point onward, I can see and work through the steps. If I were to add these two equations, then I get y = mx + m + 2b - 36. I figure there's substitution occurring for their simplification, but I'm oblivious to it. edit: Oh jeez, and I posted this in the wrong subsection. Should I re-post it, or will this be moved? Sorry about that!