Answer
See graph, $(2,3)$ and $(3,2)$
Work Step by Step
Step 1. Graph the given equations
$\begin{cases} (y-3)^2=x-2 \\ x+y=5 \end{cases}$
as shown in the figure.
Step 2. We can identify the intersection points as $(2,3)$ and $(3,2)$
Step 3. Check the solutions in the first equation:
$((3)-3)^2=(2)-2=0$
and
$((2)-3)^2=(3)-2=1$
Step 4. Check the solutions in the second equation:
$(2)+(3)=5$
and
$(3)+(2)=5$
