Question

How do you solve using gaussian elimination or gauss-jordan elimination, `x-2y+z=-14`, `y-2z=7`, `2x+3y-z=-1`?

Answer 1

`x=80/7`, `y=-345/7` and `z=-124`

Explanation:

From `x-2y+z=-14`, `z=2y-x-14`

Hence `y-2*(2y-x-14)=7` or `2x-3y=-35` `(a)` and,

`2x+3y-(2y-x-14)=-1` or `3x+y=-15` `(b)`

`3x+y=-15`, `y=-3x-15`

Consequently, `2x-3*(-3x-15)=-35` and `-7x=-80`, so `x=80/7`

Thus, `y=-3*80/7-15=-345/7` and `z=2*(-345/7)-80/7-14=-124`