SOLUTION: Given the system of equations (2x - 3y - 9z = -24 |x + 3z = 6 |-3x + y - 4z = -6 ( (a) determine whether the system is inconsistent or dependent; Your answer is (input in

Algebra ->  Linear-equations -> SOLUTION: Given the system of equations (2x - 3y - 9z = -24 |x + 3z = 6 |-3x + y - 4z = -6 ( (a) determine whether the system is inconsistent or dependent; Your answer is (input in      Log On


   

Question 1175288: Given the system of equations
(2x - 3y - 9z = -24
|x + 3z = 6
|-3x + y - 4z = -6
(
(a) determine whether the system is inconsistent or dependent;
Your answer is (input inconsistent or dependent)
(b) if your answer is dependent in (a), find the complete solution. Write
x and y as functions of z.
x =


y =
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
system%282x+-+3y+-+9z+=+-24%2C%0D%0Ax+%2B+3z+=+6%2C%0D%0A-3x+%2B+y+-+4z+=+-6%29

Since y is already eliminated from the middle equation, eliminate y
from the first and third equations by multiplying the third one by 3,
and adding term by term:

 2x - 3y -  9z = -24
-9x + 3y - 12z = -18
--------------------
-7x      - 21z = -42

Let's divide that through by -7

 x + 3z = 6

That's the same as the 2nd equation, so it is a dependent system.

Solve that for x:

x = 6 - 3z

Substitute that in either of the other two original equations.  I'll pick
the first one:

       -3x + y - 4z = -6
-3(6 - 3z) + y - 4z = -6
  -18 + 9z + y - 4z = -6
       -18 + 5z + y = -6
                  y = 12 - 5z

Solution:   (x, y, z) = (6 - 3z, 12 - 5z, z)

Edwin