The system of linear equations has a unique solution. Find the solution using Ga

Algebra
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The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.

 
x + y + z = 12
x + 2y + 3z = 44
2x − y = −16
(xyz) = 
  
Apr 21st, 2015

Add the first equation to the second one; subtract the first equation multiplied by 2 from the third one:

x    + y   + z   = 12

       3y  +4z  = 56

      -3y    -2z  =-40

Add the second equation to the third one:

x    + y   + z   = 12

       3y  +4z  = 56

               2z  = 16

Then from the third equation z = 16/2 = 8, from the second equation y = (56-4z)/3 = (56-32)/3  = 24/3 = 8, from the first equation x = 12 - y - z = 12 - 8 - 8  = -4.

Answer: (-4, 8, 8).  

Apr 21st, 2015

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