`2x + 2y - z = 2, x - 3y + z = -28, -x + y = 14.` Use matricies to solve the system of equations (if possible). Use Gauss-Jordan elimination.

`2x+2y-z=2`

`x-3y+z=-28`

`-x+y=14`

The equations can be written as,

`[[2,2,-1,|2],[1,-3,1, |-28],[-1,1,0,|14]]`

R2`->` R1+R2+R3

`[[2,2,-1,|2],[2,0,0,|-12],[-1,1,0,|14]]`

R1 `->` R1-R2

`[[0,2,-1,|14],[2,0,0,|-12],[-1,1,0,|14]]`

R3 `->` 2R3+R2

`[[0,2,-1,|14],[2,0,0,|-12],[0,2,0,|16]]`

R1`->` R1-R3

`[[0,0,-1,|-2],[2,0,0,|-12],[0,2,0,|16]]`

Now,

`-z=-2`

`:.z=2` 

`2x=-12`

`x=-12/2=-6`

`2y=16`

`y=16/2=8`

So, the solutions are x=-6,y=8,z=2