Question

How do you solve each system of equations?

1. 4x - 4y + 4z = - 4
4x + y - 2z = 5
-3x - 3y - 4z = -16

Answer 1

`x=1,y=3,z=1`

Explanation:

`4x-4y+4z=-4`

`4x=-4+4y-4z`

`x=-1+y-z`

Substitute
`x=-1+y-z` into second equation:

`4\left(-1+y-z\right)+y-2z=5`

`-4+4y-4z+y-2z=5`

`5y-6z-4=5`

`y=(6z+9)/(5)`

Substitute
`x=-1+y-z` and
`y=(6z+9)/(5)` into the third equation:

`(-41z-54)/(5)+3=-16`

`-41z-54=-95`

`z=1`

Substitute
`z=1` into
`y=(6z+9)/(5)`:

`y=3`

Plug in y and z values into
`x=-1+y-z`:

`x=1`