Suppose two systems of linear equations are equivalent but not identical. Which of the following MUST be true about the systems? Choose ALL that apply.

A

You can rearrange the the equations of one system to get the other system.

B

Each equation in the first system is a non-zero multiple of an equation in the second system.

C

The two systems have exactly the same set of solutions.

D

Either both systems are consistent or both systems are inconsistent.