System of linear equations problem

I am pretty much stuck at this SLE question, as I am not exactly sure how to use my graphic calculator to solve for x, y and z:

x+y+z = 2a   

2x-y+z = 3a-2b

x-2z = 2b-a     

where a and b are unknown constants.

Student X

There is no need to use the graphic calculator for this. The problem is uniquely designed-how so?

x+y+z = 2a   -----------------(1) 

2x-y+z = 3a-2b  -------------(2) 

x-2z = 2b-a   ----------------(3)

(1)+(2)+(3): you get 4x = 4a =======> x = a;

with this, it isn't hard to discover that  y =b  and   z = a-b   (shown)

Hope this helps. Peace. 

Best Regards,

Mr Koh