Answer
$(1,4)$.
Work Step by Step
We are given:
$y=-x^2+4x+1$ and $y=2x+2$
Graph both equations in the same coordinate plane.
The graph is shown in the image file.
The point of intersection is $A=(1,4)$.
Hence, the solution of the system is $(1,4)$.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/8d446b64-bb02-4356-8af1-1a546001ea0c/steps_image/small_1646667495.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001916Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=e9d37233a09f93145d9180ae02f794dea99b756dc90b2a3a0e022b5ebcb94a53)