# Solve this equation using the Gaussian or Gauss-Jordan elimination x+9y+8z=0 5x+8y+z=35 x-4y-z=17

You need to reduce the system to triangular form, hence, you should, eliminate x from the first and second equation such that:

-5x - 45y - 80z + 5x + 8y + z = 0 + 35

-37y - 79z = 35

You need to eliminate x from the first and the third equation such that:

x + 9y + 8z - x - 4y - z= 0-17

5y + 7z = -17

You need to use the equation -37y - 79z = 35 and the equation 5y + 7z = -17 to eliminate y such that:

`{(-37y - 79z = 35),(5y + 7z = -17):}`

`{(-185y- 395 z = 175),(185y + 259z = -629):}`

-136z=-454 => z = 454/136

The next step of finding solution y is as it follows:

You need to substitute `454/136` for z in equation `5y + 7z = -17` such that:

`5y + 7*454/136 = -17`

`5y = -17 - 3178/136`

`5y = (-2312-3178)/136 => y = 5490/680 => y = 549/68`

You need to substitute `549/68` for y in equation `x+9y+8z=0` such that:

`x = -9*549/68 - 8*454/136`

`x = (-9882-3632)/136 => x = -13514/136`

Hence, evaluating the solution to the system of equation using Gaussian elimination yields `x = -13514/136 , y = 549/68, z = 454/136.`

Approved by eNotes Editorial Team