Please share your efforts - not in words but mathematical steps.
That process doesn't sound helpful.
I have tried this method, and this is how I get it. Did you mean that I need to make X2 a subject in the equation that I'm currently trying to solve?That process doesn't sound helpful.
You need to eliminate X1 and X2 from the three equations. One way would be to solve equation 1 for X1 (in terms of X2 and X3) and put that into equations 2 and 3. Now you've eliminated X1 entirely. Then do similarly with the new equations to eliminate X2 as well.
It may help you keep track of things if you temporarily define constants so you can write equation 1 as AX1 = BX2 + CX3, and similarly elsewhere.
If you missed an X1 in the stage where you should have been eliminating it, then you really need to go back and fix that. If you haven't eliminated a variable, then you've accomplished nothing.