Question 1197030
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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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    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.


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


<U>CHECK</U>.  I checked this solution by substituting the found values into original equations and got confirmation.
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Solved.