Answer
Both points $(4, 3)$ and $(-1,-7)$ are solution of the system.
Work Step by Step
We are given two system of equations: $2x^2=3y+23 \ and \ y=2x-5$
As depicted in the graph, there are two points $(4,3)$ and $(-1,-7)$.
Our next step is to check the points satisfy both equations.
Plug $x=4$ and $y=3$ in the given equations of system to obtain:
$(2)(16)=9+23\implies 32=32 (True)\quad and \quad y=2x-5 \ or, 3=8-5 \implies 3 = 3 (True)$
This implies that the point $(4,3)$ is the solution or point of intersection of graphs.
Now, plug $x=-1$ and $y=-7$ in the given equations to obtain:
$ (2)(-1)^2=-21+23\implies 2=2 (True)\quad and \quad -7=-2-5 \implies -7 = -7 (True)$
This implies that the point $(4, 3)$ is the solution or point of intersection of graphs.
Therefore, both points $(4, 3)$ and $(-1,-7)$ are solution of the system.
