solve the system

Question

7x^2 - 5y^2 + 20y = 3
21x^2 + 5y^2 =209

Answer 1

since 7x^2 = 5y^2 - 20y + 3

21x^2 = 15y^2 - 60y + 9

plug that into the 2nd equation to get

20y^2 - 60y - 200 = 0
y^2 - 3y - 10 = 0
(y-5)(y+2) = 0

From there you can see that the circle and the hyperbola intersect at

(3,-2) (-3,-2) (2,5) (-2,5)