hi, i'm practicing proofs for an upcoming test regarding systems of linear equations, matrices, and Gaussian elimination. i was wondering if anyone could show me how to do the following that i found in my textbook in case i'm asked to do a similar one:

Prove that if more than one solution in 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 these solutions are different).