How many solutions does the system have? y=−2x+1y=−2x2+1?

Set the equations to equal each other:
-2x²+1=-2x+1

Solve for x:

-2x²+1=-2x+1
-2x²+2x+1=-2x+2x+1
-2x+2x+1-1=1-1
-2x²+2x=0
2x (-x+1)=0

2x=0 and -x+1=0
2/2x=0/2 -x+x+1=0+x
x=0 1=x

There are two solutions, x=0,1