SOLUTION: -6x-2y+2z=-8 3x-2y-4z=8 6x-2y-6z=-18

Algebra ->  Systems-of-equations -> SOLUTION: -6x-2y+2z=-8 3x-2y-4z=8 6x-2y-6z=-18      Log On


   



Question 1079713: -6x-2y+2z=-8
3x-2y-4z=8
6x-2y-6z=-18

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

-6x-2y%2B2z=-8...........eq.1
3x-2y-4z=8...........eq.2
6x-2y-6z=-18 ...........eq.3
-----------------------------------------------
6x-2y-6z=-18 ...........eq.3
-6x-2y%2B2z=-8...........eq.1
--------------------------------------------------add both
6x-2y-6z-6x-2y%2B2z=-18-8
cross%286x%29-2y-6z-cross%286x%29-2y%2B2z=-26
-4y-4z=-26.....divide both sides by -4
y%2Bz=6.5............solve for y
y=6.5-z............(a)

3x-2y-4z=8...........eq.2...............both sides multiply by 2
-6x-2y%2B2z=-8...........eq.1
...........................................................
6x-4y-8z=16...........eq.2
-6x-2y%2B2z=-8..........eq.1
------------------------------------------add
6x-4y-8z-6x-2y%2B2z=16-8
-6y-6z=8
-6y-6z=8..divide both sides by -6
y%2Bz=-8%2F6
y%2Bz=-1.333333333333333........solve for y
y=-1.33-z...........(b)
use (a) and (b) to find z
y=6.5-z...........(a)
y=-1.33-z...........(b)
-------------------------------------------- left sides same, so =>
6.5-z=-1.33-z
6.5%2B1.33=z-z
6.5%2B1.33=0

The system is inconsistent, no+solution exists.