How to solve a really nasty system of nonlinear equations?

Determine the real solutions to the system of nonlinear equations.?

• Determine the real solutions to the system of nonlinear equations. x^(2)+y^(2)=1 x^(2)+(y+1)^(2)=4 Give the solution set. Type an ordered pair. Type an exact answer, using radicals as needed. Can you please explain how to solve this. Thanks

• Answer:

  First expand both equations: x^2 + y^2 = 1 Rearrange the above equation to isolate y^2=1-x^2 x^2 + y^2 + 2y + 1 = 4 Plug the rearranged equation 2 lines above into y^2 in the above equation x^2+1-x^2 + 2y + 1 = 4 2y=2 y=1 Now solve for x by plugging this y value into either of the 2 equations that you were given in the question: x^2 + 1^2 = 1 x=0 So the solution set is (1,0)