Question

How do you solve the system of equations`-8x+5y=-8` and `-16x-y=-16` by elimination?

Answer 1

`x=1` and `y=0`

Explanation:

`2*(-8x+5y)-(-16x-y)=2*(-8)-(-16)`

`-16x+10y+16y+y=-16+16`

`11y=0`, so `y=0/11=0`

Hence,

`-8x+5*0=-8`

`-8x=-8`, thus `x=(-8)/(-8)=1`

Answer 2

`x=1 and y=0`

Explanation:

The perfect scenario for the elimination method is if one of the variables can be additive inverses.

Multiply the first equation by `-2` to achieve this:

`color(white)(xxxxxxxxxxx)-8x+5y" "=-8" "....A`
`color(white)(xxxxxxxx.xxx)color(blue)(-16x)-y" "=-16" "....B`
`A xx -2:color(white)(xxxxx.x)color(blue)(16x)-10y =+16" "....C`

`B+C: color(white)(xxxxxxxx.x)-11y =0`

`color(white)(xxxxxxxxxxxxxxxxx.x)y =0`

If `y=0` then `-8x =-8`

Which gives `x =1`