1. The problem statement, all variables and given/known data Given that the values for a, b, c, d, e and f for the system ax+by=e, cx+dy=f has two different solutions. Show that ax+by=0, cx+dy=0 also has two different solutions. 2. Relevant equations 3. The attempt at a solution There're three cases of how two straight lines can intersect: (i) At only 1 point: unique solution (ii) They are parallel and do not intersect: no solution (iii) They are the same line: infinitely many solutions I assume by two, it means infinitely many solutions? Hence, the matrix [a b; c d] is singular? I think I need to use row equivalent or equivalent matrix for this? Thanks.