Answer
$(-2,0), (2,0)$
Work Step by Step
We are given the curves:
$\begin{cases}
x^2-y^2=4\\
x^2+y^2=4
\end{cases}$
The equation $x^2-y^2=4$ represents a horizontal hyperbola centred in origin. The equation $x^2+y^2=4$ represents a circle centered in origin and having radius 2.
We graph both curves.
From the graph we find the intersection points:
$(-2,0)$ and $(2,0)$
We check if both points check the equations:
$(-2,0)$
$x^2-y^2=4$
$(-2)^2-0^2\stackrel{?}{=}4$
$4=4\checkmark$
$x^2+y^2=4$
$(-2)^2+0^2\stackrel{?}{=}4$
$4=4\checkmark$
$(2,0)$
$x^2-y^2=4$
$2^2-0^2\stackrel{?}{=}4$
$4=4\checkmark$
$x^2+y^2=4$
$2^2+0^2\stackrel{?}{=}4$
$4=4\checkmark$
So the system's solutions are:
$(-2,0), (2,0)$
