Solutions in Tandem A student who was asked to solve two systems, and noticed that they di...

Solutions in Tandem A student who was asked to solve two systems,

and

noticed that they differed only in their right-hand sides. She formed the matrix

and obtained its RREF using Gauss-Jordan elimination:

She concluded that the solutions of the two systems were given, respectively, by the vectors

and .

Explain why this is correct.