the question itself does not appear to make sense if only lamda and mu are to be solved. equation (1) seems to be useless here.
These sorts of questions test your understanding of systems of linear equations. You can't just use Google and get pages telling you about all the different types of questions that can be asked, you have to actually understand the basic theory behind solving systems of linear equations and the types of solutions that are possible.
Regardless of what mode of study your enrolled in, surely you get notes. And those notes would include the theory that is required to understand how to tackle questions like this, or at least sufficient theory to provide you with relevant key words that you can use for a Google search. It is not the role of MHF to provide on-line tuition. The role of MHF is to provide help with specific questions. That help has been amply given in this thread.
Thread closed.