I would like to know how I can manipulate a system of three equations, and three variables, so that it boils down to an expression containing only one variable. As an end result, I would like to get the equation that is to be solved rather than a solution itself.
Is that possible using Wolfram Alpha?
You may try “eliminate”.
Try something like
eliminate {x,y} from {3x+4y+11z=9,2x-5y-3z=2,5x-4y+3z=11}
which returns
11x= -18
My apologies for my mistake, that should have been
11z= -18