SOLUTION: 4x+3z=4 2y-6z=-1 8x+4y+3z=9 first i added equations 1 &2, But since the equations don't have the same variables i substituted the missing variables with zero.

Remember, the idea is to have the SAME variable
missing in two equations, not just to eliminate
any variable you can.

You should start either of the following two 
ways, but not the way you started.  

1. Take advantage of the fact that y is already 
missing in the 1st equation. To do so, use the other 
two equations, 2nd and 3rd, to get another 
equation with y missing.  Then solve that with
the 1st.

or

2. Take advantage of the fact that x is already 
missing in the 2nd equation. To do so, use the other 
two equations, 1st and 3rd, to get another 
equation with x missing.  Then solve that with
the 2nd.

I'll arbitrarily choose the first way.

Since y is already eliminated in the first equation,

let's put it aside for now, and use only the other two
equations to eliminate y, the same variable that is
missing in the first.



We'll write  as 



Remember we want to eliminate y, so we multiply
the upper equation through by  and add
it to the lower equation:



We add term by term and get



Now we go back and get the very first original
equation which we put aside, 

We put it together with the one we just found
and now we have a system of two equations with 
the SAME missing variable, y. 

 

Now we eliminate  by multiplying the
upper equation through by -2, and adding:



and get





Substitute this into 







Now substitute these values in either one of the 
original equations which contains . The 
simpler one is 







So the solution is , , 

Edwin