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

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Answer 1 · 2016-10-30T02:01:37

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

Given:

$y^{2} = x^{2} - 25$ $y^2 = x^2 - 25$ [1]
$x^{2} - y^{2} = 7$ $x^2 - y^2 = 7$ [2]

Substitute $x^{2} - 25$ $x^2 - 25$ for $y^{2}$ $y^2$ in equation [2]

$x^{2} - (x^{2} - 25) = 7$ $x^2 - (x^2 - 25) = 7$

$25 = 7$ $25 = 7$

This indicates the the two hyperbolas do not intersect.

How do you find the exact solutions to the system y2=x2−25y^2=x^2-25 and x2−y2=7x^2-y^2=7?