Answer
$(\sqrt 5, 2)$
$(\sqrt 5, -2)$
$(-\sqrt 5, 2)$
$(-\sqrt 5, -2)$
Work Step by Step
Given the system of equations:
1. $x^2 + y^2 = 9$
2. $x^2 - y^2 = 1$
It asks to find all solutions.
Add equation one and two
$2x^2 = 10$
$x^2 = 5$
$x = +/- \sqrt 5$
Substitute the values into the equation
$(\sqrt 5)^2 + y^2 = 9$
$y^2 = 4$
$y = 2, -2$
$(-\sqrt 5)^2 + y^2 = 9$
$y^2 = 4$
$y = 2, -2$
All solutions:
$(\sqrt 5, 2)$
$(\sqrt 5, -2)$
$(-\sqrt 5, 2)$
$(-\sqrt 5, -2)$
