Suppose we have a system of 2 equations in 2 unknowns x,y: a1x+b1y=c1 a2x+b2y=c2 If the determinant of [a1 b1 a2 b2] is nonzero, then the solution to the system exists and is unique. [I am OK with this] If the determinant of [a1 b1 a2 b2] is zero, this does not distinguish between the cases of no solution and infinitely many solutions. To gain some insight, we need to further check the determinatnts of [a1 c1 a2 c2] and [b1 c1 b2 c2] If both determinants are zero, then the system has infinitely many soltuions. If at least one of the two determinants are nonzero, then the system has no solution. =================================== Is the bolded part correct or not? I don't see why it is true. How can we prove it? Thanks for any help!