Examine the system of equations below. Predict the number of points of intersection of the graph of this system.

$x^{2} + y^{2} = 20\\ \left(x − 6\right)^{2} + y^{2} = 32$

1. Solve the system algebraically to determine if your prediction was correct.

   Hint (a):

   To solve algebraically, solve the top equation for $y^2$ and then substitute.

2. If you have not already done so, sketch a graph of the system of equations. Does the graph confirm your answer to part (a)?

   Hint (b):

   The circles should intersect twice.