I am using Hawkes Learning System (8.7 Nonlinear Systems of Equations)and my problem is x^2+y^2=13 and y+7=x^2. The answers I came up with are 2 square root of 3 and 3 for my x's. And I received (5,-4) as the y-coordinates. Is this correct?

Answer 1

since x^2 = y+7,

(y+7) + y^2 = 13
y^2 + y - 6 = 0
(y+3)(y-2) = 0
y = -3 or 2
so, x = ±2 or ±3
the solutions are
(-3,2)(3,2)(2,-3)(-2,-3)

How did you arrive at your results?