SOLUTION: -3x+6z=-3 6x+5y=-3 -y+5z=-13

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: -3x+6z=-3 6x+5y=-3 -y+5z=-13      Log On


   

Question 1152656: -3x+6z=-3
6x+5y=-3
-y+5z=-13
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
-3x%2B6z=-3.............1)
6x%2B5y=-3.............2)
-y%2B5z=-13.............3)
---------------------------------

-3x%2B6z=-3.............1)........both sides multiply by 2
6x%2B5y=-3.............2)
----------------------------------------------

-6x%2B12z=-6.............1)
6x%2B5y=-3.............2)
------------------------------------------add

-6x%2B12z%2B6x%2B5y=-6-3
12z%2B5y=-9 ..........solve for z
12z=-5y-9
z=-5y%2F12-9%2F12 ........1a)


-y%2B5z=-13.............3).........solve for z
5z=y-13
z=y%2F5-13%2F5........2a)

from 1a) and 2a) we have

-5y%2F12-9%2F12=y%2F5-13%2F5.......solve for y
5%28-5y-9%29=12%28y-13%29
-25y-45=12y-156
156-45=12y%2B25y
111=37y
y=3

find z
z=3%2F5-13%2F5........2a)
z=-10%2F5
z=-2

go to
-3x%2B6z=-3.............1), plug in z
-3x%2B6%28-2%29=-3
3-12=3x
3x=-9
x=-3

solutions:
x=-3,y=3,z=-2


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

-3x+6z=-3
6x+5y=-3
-y+5z=-13
If you wish to TORTURE yourself then go along with the way the person who claims to be a MATHLOVER, shows the solutions. Otherwise, do this problem as follows:

 - 3x       + 6z = - 3 ------ eq (i)

   6x + 5y       = - 3 ------ eq (ii)

        - y + 5z = - 13 ----- eq (iii)

 - 6x       + 12z = - 6 ------ Multiplying eq (i) by 2 ------ eq (iv)

        5y  + 12z = - 9 ------ Adding eqs (iv) & (ii) ------- eq (v)

      - 5y  + 25z = - 65 ----- Multiplying eq (iii) by 5 ---- eq (vi)

              37z = - 74 ----- Adding eqs (vi) & (v)

              highlight_green%28matrix%281%2C5%2C+z%2C+%22=%22%2C+%28-+74%29%2F37%2C+%22=%22%2C+-+2%29%29



- 3x + 6(- 2) = - 3 ----- Substituting - 2 for z in eq (i)

- 3x = - 3 + 12

- 3x = 9

highlight_green%28matrix%281%2C5%2C+x%2C+%22=%22%2C+9%2F%28-+3%29%2C+%22=%22%2C+-+3%29%29



- y + 5(- 2) = - 13 ----- Substituting - 2 for z in eq (iii)

- y = - 13 + 10

- y = - 3