solve the system algebraically and graphically 32x^2+9y^2=324 3y^2-x^2=3

Answer 1

32x^2+9y^2=324
3y^2-x^2=3

Since 3y^2 = x^2+3, we have

32x^2 + 3(x^2+3) = 324

I think you can solve that fairly easily, right?

The intersections are at x=±3, y=±2.

See the graphs at

http://www.wolframalpha.com/input/?i=plot+32x^2%2B9y^2%3D324%2C+3y^2-x^2%3D3