How to solve a really nasty system of nonlinear equations?

Nonlinear System of Equations?

• Solve the nonlinear system of equations for the real solutions: x^2 + y^2 = 1 x^2 + (y+2)^2 = 9 Options: a) The solution set is ____ b) There is no solution

• Answer:

  Visualize the two circles. The first one is centered at (0, 0) and extends 1 unit each direction. Some points: (0, 1), (0, -1), (1, 0), (-1, 0) The second one is centered at (0, -2) and extends 3 units each direction. Some points: (0, -5), (0, 1), (3, -2), (-3, -2). As you see, these both have a point in common (0, 1). Since both circles are centered on the y-axis and have a point in common on the the y-axis, the circles are tangental to each other, they only have one point in common. It is (0, 1)