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

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Answer 1 · 2016-10-07T14:42:05

Let equation 1 be $y^2 = x^2 - 7$ and equation $2$ be $x^2 + y^2 = 25$ .

We know the value of $y^2$ in both equations, so we can substitute $y^2$ in equation $1$ , which is already isolated, for $y^2$ in equation $2$ .

$x^2 + (x^2 - 7) = 25$

$2x^2 = 32$

$x^2 = 16$

$x = +- 4$

$y^2 = 4^2 - 7" AND "y^2 = -4^2 - 7$

$y^2 = 9" AND "y^2 = 9$

$y = +-(3)" AND "y = +-(3)$

$:.$ The solution is $(+-4, +-3)$

Hopefully this helps!

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