Systems of Polynomial Equations Practice Test

A designer models a ramp by the line $y=\tfrac{1}{2}x+1$ and an arch above it by the parabola $y=-\tfrac{1}{2}x^2+2x+1$. The ramp meets the arch at the intersection points. What is the product of the $x$-coordinates of the intersection points?

On the coordinate plane, the graphs of the line $y=x+1$ and the parabola $y=x^2-1$ are shown. How many solutions does the system have (how many intersection points are there)?