Question

How do you solve `3x + 6z = 0`, `-2x + y = 5`, `y + 2z = 3`?

Answer 1

`(x,y,z)=(-2,1,1)`

Explanation:

Given
[1]`color(white)("XXX")color(white)(+)3xcolor(white)(+0y)+6z=0`
[2]`color(white)("XXX")-2x+color(white)(1)ycolor(white)(+0z)=5`
[3]`color(white)("XXX")color(white)(+0x+1)y+2z=3`

Statement [2]`rarr`
[4]`color(white)("XXX")y=2x+5`

Substituting from [4] into [3]
[5]`color(white)("XXX")2x+5+2z=3`
Simplifying
[6]`color(white)("XXX")2x+2z=-2`
or
[7]`color(white)("XXX")x+z=-1`
or
[8]`color(white)("XXX")z=-x-1`

Substituting from [8] into [1]
[9]`color(white)("XXX")3x+6(-x-1)=0`
Simplifying
[10]`color(white)("XXX")-3x=6`
or
[11]`color(white)("XXX")x=-2`

Substituting from [11] into [8]
[12]`color(white)("XXX")z=-(-2)-1=+2-1=1`

Substituting from [11] into [4]
[13]`color(white)("XXX")y=2(-2)+5=-4+5=1`