Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate
system and finding points of intersection.
-$$\begin{array} { l }
x ^ { 2 } - y ^ { 2 } = 9 \
x ^ { 2 } + y ^ { 2 } = 9
\end{array}$$

A) $\{ ( 3,0 ) , ( - 3,0 ) \}$
B) $\{ ( 0,3 ) , ( 0 , - 3 ) \}$
C) $\{ ( 3,0 ) \}$
D) $\{ ( 0,3 ) \}$

Question

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate
system and finding points of intersection.
-$$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 9 \
x ^ { 2 } + y ^ { 2 } = 9
\end{array}$$

A) $\{ ( 3,0 ) , ( - 3,0 ) \}$ 
B) $\{ ( 0,3 ) , ( 0 , - 3 ) \}$ 
C) $\{ ( 3,0 ) \}$ 
D) $\{ ( 0,3 ) \}$

Quizplus · Accepted Answer

To solve this system, we can start by graphing both equations in the same rectangular coordinate system.

The first equation, $x^2 - y^2 = 9$, is the equation of a hyperbola centered at the origin with vertices at $(\pm 3, 0)$ and asymptotes given by the lines $y = \pm \frac{x}{3}$.

The second equation, $x^2 + y^2 = 9$, is the equation of a circle centered at the origin with radius 3.

Graphing both of these equations in the same coordinate system, we get:

11ecbe13_c236_0a14_88d3_c5cb22fe25cd.png

We can see that the two curves intersect at the points $(3, 0)$ and $(-3, 0)$. Therefore, the solution set for the system is $\{(3, 0), (-3,0)\}$.

So, the best choice is A) $(3,0),(-3,0)$ because it correctly identifies the solution set as the points of intersection.

Find the Solution Set for the System by Graphing Both x2−y2=9x2+y2=9\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 9 \\x ^ { 2 } + y ^ { 2 } = 9\end{array}x2−y2=9x2+y2=9​

Find the Solution Set for the System by Graphing Both $\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 9 \\x ^ { 2 } + y ^ { 2 } = 9\end{array}$