Answer
Both points $(-6, 3)$ and $(3,-6)$ are solution of the system.
Work Step by Step
We are given two system of equations: $x+y=-3 \ and \ x^2+y^2=45$
As depicted in the graph, there are two points $(-6, 3)$ and $(3,-6)$.
Our next step is to check the points satisfy both equations.
Plug $x=-6$ and $y=3$ in the given equations of system to obtain:
$-6+3=-3 \implies -3= -3 (True)\quad and \quad , (-6)^2+(3)^2=45 \implies 45 = 45 (True)$
This implies that the point $(-6, 3)$ is the solution or point of intersection of graphs.
Now, plug $x=3$ and $y=-6$ in the given equation of system to obtain:
$ 3-6=-3 \implies -3=-3 (True)\quad and \quad 9+36=45 \implies 45 = 45 (True)$
This implies that the point $(3, -6)$ is the solution or point of intersection of graphs.
Therefore, both points $(-6, 3)$ and $(3,-6)$ are solution of the system.
