Answer
$(0,-3), (0,3)$
Work Step by Step
We are given the curves:
$\begin{cases}
9x^2+y^2=9\\
y^2-9^2=9
\end{cases}$
The equation $9x^2+y^2=9$ represents an ellipse centered in origin. The equation $y^2-9y^2=9$ represents a hyperbola centered in origin.
We graph both curves.
From the graph we find the intersection points:
$(0,-3)$ and $(0,3)$
We check if both points check the equations:
$(0,-3)$
$9x^2+y^2=9$
$9(0^2)+(-3)^2\stackrel{?}{=}9$
$9=9\checkmark$
$y^2-9x^2=9$
$(-3)^2+9(0^2)\stackrel{?}{=}9$
$9=9\checkmark$
$(0,3)$
$9x^2+y^2=9$
$9(0^2)+3^2\stackrel{?}{=}9$
$9=9\checkmark$
$y^2-9x^2=9$
$3^2+9(0^2)\stackrel{?}{=}9$
$9=9\checkmark$
So the system's solutions are:
$(0,-3), (0,3)$
