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
