How do you find the exact solutions to the system $x^{2} + y^{2} = 64$ $x^2+y^2=64$ and $x^{2} + 64 y^{2} = 64$ $x^2+64y^2=64$ ?

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Answer 1 · 2016-11-10T23:42:57

Please see the explanation for steps leading to the points $(- 8, 0) and (8, 0)$ $(-8, 0) and (8,0)$

Given:

$x^{2} + y^{2} = 64 [1]$ $x^2 + y^2 = 64" [1]"$
$x^{2} + 64 y^{2} = 64 [2]$ $x^2 + 64y^2 = 64" [2]"$

Subtract equation [1] from equation [2]:

$63 y^{2} = 0$ $63y^2 = 0$

$y = 0$ $y = 0$

$x^{2} = 64$ $x^2 = 64$

$x = \pm 8$ $x = +-8$

The solutions are the points $(- 8, 0) and (8, 0)$ $(-8, 0) and (8,0)$

How do you find the exact solutions to the system x2+y2=64x^2+y^2=64 and x2+64y2=64x^2+64y^2=64?