Scattering in Finite step potential

[Guaicai]

origin page : http://www.physicspages.com/2012/08/08/finite-step-potential-scattering/
No quite understand how the solution

come from this equation

 

[Simon Bridge]

Solve for B and D in terms of A and simplify.

 

[vela]

If you want to solve for B and D in terms of A, you have a linear system with two equations and two unknowns, e.g., x+y=4, 2x-3y=0, but the constants look complicated.