Question 130320
You have 3 equations, call them A, B, and C.  First, combine A and B, eliminating z, to get an equation with x and y.  Then combine B and C, again eliminating z, to get another equation with x and y.  Then you will have a system with 2 equations and 2 variables, which you should know how to solve already.
Adding A and B gives 7x-y=6 (call this D).  Adding B and C gives 9x-y=13 (call this E).  Change equation D to y=7x-6.  Now plug that y into E to get 9x-(7x-6)=13, so 2x+6=13, so 2x=7, so x=3.5.  plug that back into D to get y=7(3.5)-6=24.5-6 =18.5.  Using equation B, z=2x-3y-17=2(3.5)-3(18.5)-17= 7-55.5-17= -48.5-17=-65.5
So (x, y, z)=(3.5, 18.5, -65.5).