Question

what are the solutions to the nonlinear system of equations?

Answer 1

Given
x^2+y^2=9  ................(1)
x^2/3^2-y^2/3^2=1......(2)

Multiply (2) by 9 on both sides to give
x^2-y^2=9..................(2a)

Then (1) and (2a) make a "sum and difference" problem, where
x^2=(9+9)/2=9   => x=+3 or -3
y^2=(9-9)/2 = 0  => y=0
which gives us the solutions
(x,y)={(3,0),(-3,0)}