Question 1002469
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3x + 2y - 8z =  29
9x -  y + 2z =  23
-x - 2y + 8z = -11
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So, your original system of equation is

    3x + 2y - 8z =  29    (1)
    9x -  y + 2z =  23    (2)
    -x - 2y + 8z = -11    (3)


Add equations (1) and (3).  The terms with 'y' and 'z' will cancel each other, and you will get then

    3x - x = 29 - 11,  --->  2x = 18,  --->  x = 18/2 = 9.


Now substitute this value x = 9 into the first and second equations

    3*9 + 2y - 8z = 29     (1')
    9*9 -  y + 2z = 23     (2')


Simplify

          2y - 8z =   2    (1'')
          -y + 2z = -58    (2'')


Now we are on the straight finish line: we only need to solve one 2x2-syatem of equations (1''), (2'').

Solve it by the Elimination method. For it, multiply equation (2'') by 2 (both sides) and add to equation (1'').
You will get

             - 8z + 4z = 2 + 2*(-58),  --->  -4z = -114,  z = (-114)/(-4) = 28.5.


Now from equation (2'')

           y = 58 + 2*28.5 = 115.


<U>ANSWER</U>.  The solution to the given system is x= 9,  y = 115,  z = 28.5.
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Solved.