Question

How do you solve `x - 9y = -80` and `2y - 2x = 16` using substitution?

Answer 1

`(x,y)to(1,9)`

Explanation:

`x-9y=-80to(1)`

`2y-2x=16to(2)`

`"rearrange equation "(1)" expressing x in terms of y"`

`x=-80+9yto(3)`

`color(blue)"substitute "x=-80+9y" in equation "(2)`

`2y-2(-80+9y)=16`

`2y+160-18y=16`

`-16y+160=16`

`"subtract 160 from both sides"`

`-16y=16-160=-144`

`"divide both sides by "-16`

`y=(-144)/(-16)=9`

`"substitute "y=9" in equation "(3)`

`x=-80+81=1`

`"solution is "(x,y)to(1,9)`
graph{(y-1/9x-80/9)(y-x-8)=0 [-20, 20, -10, 10]}