Question

Steps to solving this in elimination

Answer 1

`x=-5,y=-1,z=0`

Explanation:

First, let's subtract 3x-6y+4z=-9 from 4x-6y-5z=-14

`3x-6y+4z=-9\\-(4x-6y-5z=-14)\\---------------------------\\-x+9z=5`

Then, we can add -9x+6x+12z=39 to 3x-6y+4z=-9

`-9x+6y+12z=39\\+ 3x-6y+4z=-9\\-----------------------\\-6x+8z=30`

After that, we can solve the two as a system of equations

`-x+9z=5\\-6x+8z=30\\Make-the-x's-equal\\-6x+54z=30\\-(-6x+8z=30)\\----------------------\\46z=0\\z=0`

Plug in z

`-x+9z=5\\-x+9(0)=5\\-x+0=5\\-x=5\\x=-5`

Plug in x and y

`3x-6y+4z=-9\\3(-5)-6y+4(0)=-9\\-15-6y+0=-9\\-6y=6\\y=-1`

Double check

`4x-6y-5z=-14\\4(-5)-6(-1)-5(0)=-14\\-20+6+0=-14\\-14=-14\\True`