SOLUTION: 2x-3y+5z=13 4x+4y+6z=34 I want the y variable by its self.. we are supposed to solve be elimination(addition)

2x - 3y + 5z = 13
4x + 4y + 6z = 34

Since you want the y-variable by itself, get the y-terms off the
left sides and onto the right side

2x + 5z = 13 + 3y
4x + 6z = 34 - 4y

Eliminate x by multiplying the first equation by -2 and adding
it term-by-term to the second equation:

-4x - 10z = -26 - 6y
 4x +  6z =  34 - 4y
--------------------
      -4z =   8 - 10y
        z =  - y
        z = -2 + y 

Go back to

2x + 5z = 13 + 3y
4x + 6z = 34 - 4y

Eliminate z by multiplying the first equation by -6
and the second equation by 5

-12x - 30z = -78 - 18y
 20x + 30z = 170 - 20y
----------------------
  8x       =  92 - 38y 
         x =  - y
         x =  - y

So the solution with y by itself is

(x, y, z) = ( - y, y, -2 + y)

Edwin