Proof of a system of linear equations!! 1. The problem statement, all variables and given/known data Prove that if more than one solution to a system of linear equations exists, then an infinite number of solutions exists. (Hint: Show that if x1 and x2 are different solutions to AX=B, then x1 + c(x2-x1) is also a solution, for every real number c. Also, show that all these solutions are different.) 2. Relevant equations none that i know of 3. The attempt at a solution This is what i have so far, Let x1 and x2 be different solutions to Ax=B... I don't know where to go from there. How do i show that x1 + c(x2 - x1) is also a solution. Should i create an m by n matrix and then show that it works? And then how would I show that these solutions are different??? Please help. Thanks in advance.