Answer
$(\sqrt 5,2),(-\sqrt 5,2),(\sqrt 5,-2),(-\sqrt 5,-2)$
Work Step by Step
$x^{2}+y^{2} = 9$ Equation $(1)$
$16x^{2}-4y^{2} = 64$ Equation $(2)$
Multiply Equation $(1)$ by $4$ and add with Equation $(2)$
$4(x^{2}+y^{2}) + 16x^{2}-4y^{2}= 4 \times 9 +64$
$4x^{2}+4y^{2} + 16x^{2}-4y^{2}= 36 +64$
$20x^{2}= 100$
$x^{2}= 5$
$x = ±\sqrt 5$
$x = \sqrt 5$ or $x = -\sqrt 5$
Substitute $ x$ values in Equation $(1)$
Let $x = \sqrt 5$
$x^{2}+y^{2} = 9$
$(\sqrt 5)^{2}+y^{2} = 9$
$5+y^{2} = 9$
$y^{2} = 9-5$
$y^{2} = 4$
$y = ±\sqrt 4$
$y = ±2$
Let $x = -\sqrt 5$
$x^{2}+y^{2} = 9$
$(-\sqrt 5)^{2}+y^{2} = 9$
$5+y^{2} = 9$
$y^{2} = 4$
$y = ±2$
$(\sqrt 5,2),(-\sqrt 5,2),(\sqrt 5,-2),(-\sqrt 5,-2)$ all four ordered pair satisfy the given equations. So, the solutions are $(\sqrt 5,2),(-\sqrt 5,2),(\sqrt 5,-2),(-\sqrt 5,-2)$
