Question

3x+y-z=3
2x-8y+z=-5
x-2y+9z=8
solve by gauss elimination method
$ax = b$
​

Answer 1

Answer:

3x + y - z = 3

2x - 8y - 9z = -5

x - 2y + 9z = 8

(Solve equation [3] for the variable  x )

[3]    x = 2y - 9z + 8

(put this in for variable  x  in equation [1])

      3•(2y-9z+8) + y - z = 3

     7y - 28z = -21

(put this in for variable  x  in equation [2])

    2*(2y-9z+8) - 8y - 9z = -5

       - 4y - 27z = -21

(Solve equation [1] for the variable  y )

 

     7y = 28z - 21

   y = 4z - 3

(put  this in for variable  y  in equation [2])

    - 4•(4z-3) - 27z = -21

    - 43z = -33

(Solve equation [2] for the variable  z )

      43z = 33  

      z = 33/43  

( By now we know this much :

   x = 2y-9z+8

   y = 4z-3

   z = 33/43

Use the  z  value to solve for  y  

   y = 4(33/43)-3 = 3/43  

( Use the  y  and  z  values to solve for  x )

 x = 2(3/43)-9(33/43)+8 = 53/43  

Solution :

therefore,

x,y,z = 53/43, 3/43, 33/43

Step-by-step explanation:

Hope it helps.