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How to solve a really nasty system of nonlinear equations?

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  • Solve the nonlinear system of equations for real solutions. x^2 + y^2 = 9 x^2 + (y-1)^2 = 4 Options: a) The solution set is ____ b) There is no solution

  • Answer:

    x^2 = 9 - y^2 x^2 = 4 - (y - 1)^2 9 - y^2 = 4 - (y - 1)^2 9 - y^2 = 4 - y^2 + 2y - 1 9 = 4 + 2y - 1 6 = 2y y = 3 x^2 + 3^2 = 9 x^2 + 9 = 9 x = 0 (x, y) = (0, 3)

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You can do it algebraically or graphically but I did it by sketching a graph. The answer is (0,3) and that is the only point because it is a common vertex

x^2 + y^2 = 9 x^2 + (y^2 -2y +1)=4 subtract bottom from top to eliminate (x^2) 2y -1 = 5 2y =6 y=3 sub y=3 into equation x^2 +(3)^2 =9 x^2 +9 =9 x^2 =0 y=+3 x=0

a) The solutin set is x=0, y = 3

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