Question 1167063
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x - y - z = 5        (1)
y - x - z = 1        (2)
z - y - x = -15      (3)
x * y - z = a        (4)



The problem is to find three unknowns x, y and z  from equations (1), (2) and (3)

and THEN (=after that) to find the value of "a" from equation (4).



The system of three equations (1), (2) and (3) is VERY SPECIAL, and there is  VERY SPECIAL trick to solve it.



Add equations (1), (2) and (3) (=add separately their left and right sides). You will get then

    (x+y+z) - 2x - 2y - 2z = 5+1-15,   or

     -x - y - z = -9,                  or

      x + y + z = 9.     (5)


Now add equations (1) and (5). You will get  

     2x         = 5+9 = 14;  hence,  x = 14/2 = 7.


Next, add equations (2) and (5). You will get  

    2y          = 1 + 9 = 10;  hence,  y = 10/2 = 5.


Finally, add equations (3) and (5). You will get  

    2z          = -15 + 9 = -6;  hence,  y = -6/2 = -3.


Thus  x= 7,  y= 5,  z= -3.


Hence,  a = x*y - z = 7*5 - (-3) = 35 + 3 = 38.


<U>ANSWER</U>.  x= 7,  y= 5,  z= -3,  a = 38.
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Solved.



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There are TWO MAJOR LESSONS for you to learn from my solution.


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    First is to read the problem attentively and to understand what they want from you.


    Second is this SPECIAL TRICK to solve the given system of equations.
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Happy learning (!)