Question

How do you solve y= -x and y= x+9?

Answer 1

`(x,y)to(-9/2,9/2)`

Explanation:

`y=-xto(1)`

`y=x+9to(2)`

`"since both equations express y in terms of x we can"`
`"equate the right sides"`

`rArrx+9=-x`

`"add "x" to both sides"`

`x+x+9=cancel(-x)cancel(+x)`

`rArr2x+9=0`

`"subtract 9 from both sides"`

`rArr2x=-9`

`"divide both sides by 2"`

`(cancel(2) x)/cancel(2)=(-9)/2`

`rArrx=-9/2`

`"substitute "x=-9/2" into equation "(1)`

`rArry=-(-9/2)=9/2`

`"the point of intersection "=(-9/2,9/2)`
graph{(y+x)(y-x-9)((x+9/2)^2+(y-9/2)^2-0.04)=0 [-10, 10, -5, 5]}