Question

How do you find the exact solutions to the system `x^2+y^2=25` and `2x^2+3y^2=66`?

Answer 1

`(x, y) = (+-4, +-3)`

Explanation:

These are two linear equations in `x^2 and y^2`.

The second - twice the first gives `x^2=16`, giving `x = +-4`.

Substituting in the first, `y^2=9`, giving `y =+-3`.

The solutions `(x, y) = (+-4, +-3)` give the common points of the

graphs, for the circle and the ellipse, respectively.

graph{(x^2+y^2-25)(2x^2+3y^2-66)=0x^2 [-16, 16, -8, 8]}