SOLUTION: Solve the given system of equations. / Los die gegwe stelsel van vergelykings op. (12) 4x + y + 3z = 1 8x + 9z = 10 - 6x + 3y + 12z = - 4

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Question 1197030: Solve the given system of equations. / Los die gegwe stelsel van vergelykings op. (12)
4x + y + 3z = 1
8x + 9z = 10
- 6x + 3y + 12z = - 4
Found 5 solutions by MathLover1, MathTherapy, math_tutor2020, josgarithmetic, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
........eq.1
..........eq.2
......eq.3
___________________________________________
..........eq.2, solve for

..........eq.2a

substitute in eq.1

........eq.1


............solve for
................eq.1a

go to

......eq.3, substitute and
......solve for


..........multiply by




go to
................eq.1a, substitute



go to
..........eq.2a, substitute





solutions:





Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Solve the given system of equations. / Los die gegwe stelsel van vergelykings op. (12)
4x + y + 3z = 1
8x + 9z = 10
- 6x + 3y + 12z = - 4
I hope you realize that that woman who responded is a NUT, and that a system is NEVER 
solved the way she sees fit to solve not ony this but many other systems that she "solves.".

You mst be in love with her, or maybe you're a NUT like she is, @math_tutor. Birds of a feather flock together!!
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

@MathTherapy that is extremely rude and uncalled for. I don't know why you took time out of your day to tear someone down.

Edit: No, it's called common decency which apparently you don't have. At least the students can see what kind of person you are, and so they'll know to avoid you.
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
This is not complete work and not finished:
row operation
4   1   3   1
-4  -3  0   7
-22 -1  0  -8


E2=E2-3E3

4   1   3   1
-62   0  0 -31
22  1  0  8


switch E2 & E3

4   1   3   1
22  1   0   8
-62 0   0  -31


4   1   3   1
22  1   0   8
62 0   0   31



Use E2 and known x to find
.
.
Not finished and not thoroughly checked for mistakes
Answer by ikleyn(52801)   (Show Source): You can put this solution on YOUR website!
.
Solve the given system of equations. / Los die gegwe stelsel van vergelykings op. (12)
4x + y + 3z = 1
8x + 9z = 10
- 6x + 3y + 12z = - 4
~~~~~~~~~~~~~~~~~~~~~~~~~ 

    4x + y +   3z =  1      (1)
    8x +       9z = 10      (2)
   -6x + 3y + 12z = -4      (3)


Multiply equation (1) by 2

    8x + 2y +  6z =  2.


Replace here 8x by  (10 - 9z),  based on equation (2). You will get

    (10-9z) + 2y + 6z = 2,

or

    2y -3z = -8.        (4)



Multiply equation (3) by 4

    -24x + 12y + 48z = -16.


Replace here -24x  by  -3*(10 - 9z),  based on equation (2). You will get

    -3*(10-9z) + 12y + 48z = -16,

or

    12y + 75z = 14.     (5)
    

So, you reduced the original system (1),(2),(3) to two equations (4) and (5)

     2y -  3z = -8.     (4)
    12y + 75z = 14.     (5)


Nultiply equation (4) by 6; keep equation (5) as is

    12y - 18z = -48.    (4)
    12y + 75z =  14.    (5)


Subtract equation (4) from equation(5).  The terms with "12y" will casncel each other, and you will get

          93z = 62,  giving  z = 62/93 = 2/3.


Substituting z= 2/3 into equation (5), you get

    12y + 50 = 14,  giving  12y = -36,  y = -36/12 = -3.


Substituting z= 2/3 into equation (2), you get

    8x + 6 = 10,    giving  8x = 4,  x = 4/8 = 1/2.


ANSWER.  x= 1/2,  y= -3,  z= 2/3.


CHECK.  I checked this solution by substituting the found values into original equations and got confirmation.

Solved.




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