The first and third equations are in x and z only, 
that is, neither has a y terms, so we start by taking them
as a system of 2 equations in 2 unknowns.

 

Multiply the second equation through by -2:

 

We get 

 or



Substituting in 









Substitute that in the original equation which contained y:











So the solution is (x,y,z,) = (4,-1,-2)

Edwin