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If x, y, and z are real numbers for which

x + y - z = -8

x - y + z = 18

-x + y + z = 30

 

then what is xyz?

 Nov 21, 2021
 #1
avatar+584 
+1

when I use "(i), (ii), (iii)" I'm just labeling the equations

   (i) x + y - z = -8
  (ii) x - y + z = 18
(iii) -x + y + z = 30

   (i) x + y - z = -8

  (ii) x - y + z = 18

      -------------------

                2x = 10

                  x = 5

 

    (ii) x - y + z = 18

  (iii) -x + y + z = 30

       --------------------

                   2z = 48

                     z = 24

 

        i) x + y - z = -8

    (5) + y - (24) = -8
               y - 19 = -8

                      y = 11

 

therefore xyz = 5 * 11 * 24

                      = 1320

 
 

 Nov 22, 2021
 #2
avatar+115920 
+1

Thanks Logarythm

 

Matrices are cool for working out systems of equations:

 

 Nov 22, 2021

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