Answer
Both points $(4,17)$ and $(-1,2)$ are solution of the system.
Work Step by Step
As depicted in the graph , there are two points $(4,17)$ and $(-1,2)$.
Our next step is to check the points satisfies both equations.
Plug $x=4$ and $y=17$ in the given equations to obtain:
$x^2=y-1 \ or, 16=17-1\implies 16=16 (True)\quad and \quad y=3x+5 \ or, 17=12+5 \implies 17 =17 (True)$
This implies that the point $(4,17)$ is the solution or point of intersection of graphs.
Now, plug $x=-1$ and $y=2$ in the given equations to obtain:
$x^2=y-1 \ or, 1=2-1\implies 1=1 (True)\quad and \quad y=3x+5 \ or, 2=-3+5 \implies 2 =2 (True)$
This implies that the point $(-1,2)$ is the solution or point of intersection of graphs.
Therefore, both points $(4,17)$ and $(-1,2)$ are solution of the system.
