Question

How do you find the ordered pair that is a solution to the system of equations `x + y = 10` and `x - y = 8`?

Answer 1

`x=9,y=1`

Explanation:

Adding both equations we get

`2x=18`
so `x=9`

and we get for `y`

`9+y=10`
`y=1`

Answer 2

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

Explanation:

`x+y=10to(1)`

`x-y=8to(2)`

`"adding the 2 equations term by term eliminates "y`

`x+x)+(y-y)=(10+8)`

`2x=18rArrx=18/2=9`

`"substitute "x=9" into equation "(1)`

`9+y=10rArry=10-9=1`

`"the point of intersection "=(9,1)`
graph{(y+x-10)(y-x+8)((x-9)^2+(y-1)^2-0.04)=0 [-20, 20, -10, 10]}