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

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Answer 1 · 2016-10-30T02:01:37

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

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.

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