Solve the nonlinear system of equations for real solutions X

Solve the nonlinear system of equations for real solutions. X^2 + y^2 = 1 x^2 + (y + 2)^2 = 9 The solution set is (Type an ordered pair use a comma to separate answers if needed. Type exact answers, using radicals as needed.)

Solution

x^2 + y^2 = 1

x^2 + (y + 2)^2 = 9

from eq 1

x^2 = 1 - y^2

substituting in eq 2

1 - y^2 + + (y + 2)^2 = 9

1 - y^2 + + y^2 + 2^2 + 4y = 9

4y + 5 = 9

y = 1,

using this value

x^2 = 1 - y^2

x^2 = 1 - 1^2

x^2 = 0

x = 0

Solution set will be = {(0, 1)}