Question

How do you find the exact solutions to the system `y^2=x^2-25` and `x^2-y^2=7`?

Answer 1

There are no solutions, because the two hyperbolas do not intersect.

Explanation:

Given:

`y^2 = x^2 - 25` [1]
`x^2 - y^2 = 7` [2]

Substitute `x^2 - 25` for `y^2` in equation [2]

`x^2 - (x^2 - 25) = 7`

`25 = 7`

This indicates the the two hyperbolas do not intersect.