SOLUTION: 6x+z=21 4x+6y=34 -5y+6z=-33

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Question 1152659: 6x+z=21
4x+6y=34
-5y+6z=-33
Found 3 solutions by Edwin McCravy, MathLover1, MathTherapy:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Line the equations up so that the letters line up vertically,
like this:

6x +       z =  21
4x + 6y      =  34
    -5y + 6z = -33

Notice that y is already eliminated from the first equation,
z is already eliminated from the second equation and x is
already eliminated from the third equation.  We need two
equations with the SAME letter eliminated from them.  So we
pick the easiest two equations to eliminate a letter from.
We pick the 1st and 3rd to eliminate z from:

6x +        z =  21
     -5y + 6z = -33

We multiply the top equation through by -6 to make it cancel
with the bottom equation, Then we add vertically term-by-term

-36x +      -6z = -126
       -5y + 6z =  -33
---------------------- 
-36x -  5y      = -159

Since we have eliminated z, and the original second equation also
has z eliminated we put those two together:

  4x + 6y  =   34
-36x - 5y  = -159
-----------------

We can make the x's cancel by multiplying the top equation by 9

 36x + 54y  =  306
-36x -  5y  = -159
------------------
       49y  =  147
         y  =  147/49
         y  =   3

Substitute y = 3 into 

     4x + 6y = 34
   4x + 6(3) = 34
     4x + 18 = 34
          4x = 16
           x = 4

Substitute x = 4 into the original first equation:

      6x + z = 21 
    6(4) + z = 21
      24 + z = 21 
           z = -3

So the solution is (x, y, z) = (4, 3, -3)

Edwin

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

6x%2Bz=21.............1)
4x%2B6y=34.............2)
-5y%2B6z=-33.............3)
---------------------------------
6x%2Bz=21.............1)........solve for z
z=-6x%2B21........1a)
-5y%2B6z=-33.............3)......solve for z
z=5y%2F6-33%2F6
z=5y%2F6-11%2F2........2a)

from 1a) and 2a) we have
-6x%2B21=5y%2F6-11%2F2.....solve for x
-6x=5y%2F6-33%2F6-21
-6x=%285+y%29%2F6+-+53%2F2
x=%285+y%29%2F-36+-+53%2F-12
x=+53%2F12+-+%285+y%29%2F36........3a)

go to
z=-6x%2B21........1a), substitute x
z=-6%2853%2F12+-+%285+y%29%2F36%29%2B21
z=++%285+y%29%2F6+-+11%2F2
go to
4x%2B6y=34.............3), substitute x
4%2853%2F12+-+%285+y%29%2F36%29%2B6y=34.........solve for y
%2849+y%29%2F9+%2B+53%2F3+=34

%2849+y%29%2F9++=+34-+53%2F3
%2849+y%29%2F9++=+102%2F3-+53%2F3
%2849+y%29%2F9++=+49%2F3
%2849+y%29++=+9%2849%2F3%29
%2849+y%29++=+3%2849%29
y+=+3%2849%2F49+%29
y+=+3
go to
z=5y%2F6-11%2F2........2a), substitute y
z=%285%2A3%29%2F6-11%2F2
z=5%2F2-11%2F2
z=-6%2F2
z=-3

go to
z=-6x%2B21........1a), substitute z

-3=-6x%2B21.......solve for x
6x=3%2B21
6x=24
x=4
solutions:
x+=+4, y+=+3, z+=+-3

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

6x+z=21
4x+6y=34
-5y+6z=-33
I'd advise you NEVER to consider using this woman's method to solve these equations!

It's a ridiculously "SAD" way to do these types of problems!