1. The problem statement, all variables and given/known data I am studying linear algebra independently using a pdf book online. The question I have difficulty is this: Prove that, where a, b... e are real numbers and a does not equal 0, if (1) ax + by = c has the same solution set as (2) ax + dy = e then they are the same equation. 2. Relevant equations 3. The attempt at a solution Since they are a couple of linear equations, I performed a Gaussian operation on it (1) ax + by = c (2) ax + dy = e (1) - (2) y = c-e/b-d , x = c/a - (b/a)(c-e/b-d) So basically I subtracted (1) from the (2) to get the intercept point between the equations. That should be the solution set. Since I'm trying to prove that (1) and (2) are the same, then I should let b=d and c=e. However, if b = d and c = e, then y would be 0/0. So I'm not sure what I did wrong.