Gaussian Elimination

Question

3x-4y=8z=27

Please show all steps.

9x-y-z=3

x=8y-2z=9

 

Solve by Gaussian Elimination only.

Answer 1

I am assuming that the system is actually:

 

   x + 8y - 2z = 9

  3x - 4y + 8z = 27

  9x -  y  -   z = 3

 

Multiply the first equation by -3 and add to the second equation

Multiply the first equation by -9 and add to the third equation:

 

   x + 8y - 2z = 9

      -28y+14z = 0

      -73y+17z = -78

 

Divide the second equation by -28:

 

   x + 8y - 2z = 9

          y - (½)z = 0

      -73y + 17z = -78

 

Add 73 times the second equation to the third equation:

 

   x + 8y - 2z = 9

          y - (½)z = 0

            -(39/2)z = -78

 

From the third equation, z = -78(-2/39) = 4

 

Plug into equation 2 to get y = 2

 

So, from the first equation, x + 8(2) - 2(4) = 9

 

                                                          x = 1

 

SOLUTION:  (1, 2, 4)