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

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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 = 4
2x − 3y + 2z = −2
4x + y − 3z = 3
(xyz) = 
 
 
Jul 17th, 2015

Thank you for the opportunity to help you with your question!

x + y + z = 4  --------------------(1)

2x - 3y + 2z = -2 ----------------(2)

4x + y - 3z = 3  ------------------(3)


(1) x 2 - (2)    ===>   2y - (-3y) = 8 - (-2)

    5y = 10

     y = 2

(1) x 4 - (3)     ====>  4y - y + 4z - (-3z)= 16 - 3

3y +7z = 13

3(2) + 7z = 13

7z = 7

z = 1

Plug y =2,  z = 1 into (1)

x + 2 + 1 = 4

x = 1


Therefore, x = 1, y = 2, z = 1


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 17th, 2015

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