Question

How do you find the exact solutions to the system `y=5` and `y^2=x^2+9`?

Answer 1

`y = 5`
`x=+-4`

Explanation:

First substitute `y=5` into `y^2=x^2+9`

You get: `5^2 = x^2 +9`

Square the 5 and take 9 away from both sides: `25-9=x^2`

Simplify: `16=x^2`
Therefore `x=+-sqrt(16)`
So `x=+-4`

You already know that `y = 5` and now you know that `x=+-4`

(Techincally `y = +-5` as `5^2=25` and `(-5)^2 = 25` which are the same answers.)