How do I figure this out without solving the systems of equations with Cramer's rule or the augmented matrix Gauss elimination?

Part 1: For each augmented matrix, determine which of the following statements best describes the solution to the corresponding system of equations. A) There is no solution. B] There is a unique solution. C) There are 3 solutions. D) There are infinitely many solutions with one arbitrary parameter. E) There are infinitely many solutions with two arbitrary parameters. F] There are infinitely many solutions with three arbitrary parameters. Part 2: Solve each system. 2 8 2 3 10 14 24 30 3 6