Hi Mr. Knight. I see your question is 20 days old so maybe this answer is too late. I have just started helping in the Study Group after many years on KA.

What you have above is two "simultaneous equations". There are two variables vb and vc (sorry not sure yet how to subscript).

You have two linear equations containing these two variables. The first solution step shown is to multiply the first equation by 15/10. This is chosen because it will make the coefficient of the vc term 15/100. So you can then add the two equations together to eliminate the vc term. It will be eliminated because the coefficient of the vc term in the second equation is -15/100.

That will leave a linear equation only containing the variable vb which can be solved. Then the solution value for vb can be substituted into either of the original equations to solve for vc.

Hope this helps!