`x + 2y = 0, x + y = 6, 3x - 2y = 8` Use matricies to solve the system of equations. Use Gaussian elimination with back-substitution.

The augmented matrix `[[1,2,0],[1,1,6],[3,-2,8]]`

On applying `R_2 -gt R_1 - R_2 ` we get

`[[1,2,0],[0,1,-6],[3,-2,8]]`

On applying `R_3 -gt 3R_1 - R_3 ` we get

`[[1,2,0],[0,1,-6],[0,8,-8]]`

On applying `R_3 -gt (R_3)/8` we get

`[[1,2,0],[0,1,-6],[0,1,-1]]`

On applying `R_3 -gt R_3 - R_2` we get 

`[[1,2,0],[0,1,-6],[0,0,5]]`

The corresponding system is `x + 2y = 0`

`y = -6`

`0(x) + 0(y) = 5`

No `x ` and `y ` value satisfy the last equation. 

Hence the system is inconsistent.