Answer
$(2, \sqrt 3)$
$(2, - \sqrt 3)$
$(-1, 0)$
Work Step by Step
Given the system of equations:
1. $x^2 - y^2 = 1$
2. $2x^2 - y^2 = x + 3$
It asks to find all solutions.
Subtract equation one from two
$2x^2 - y^2 = x + 3$
-($x^2 - y^2 = 1$)
$x^2 = x + 2$
$x^2 - x - 2 = 0$
$(x - 2)(x+1) = 0$
$x = 2, -1$
Substitute the values into the equation
$2^2 - y^2 = 1$
$y^2 = 3$
$y = +/- \sqrt {3}$
$(-1)^2 - y^2 = 1$
$y^2 = 0$
$y = 0$
All solutions:
$(2, \sqrt 3)$
$(2, - \sqrt 3)$
$(-1, 0)$
$(-1, -\sqrt 2)$
