Find the point(s) of intersection between the following:

x^2 + y^2 = 25
3x + 4y = 0

you know that 4y = -3x, so use that in

16x^2 + 16y^2 = 400
16x^2 + (4y)^2 = 400
16x^2 + 9x^2 = 400

and I think you can take it from there, right?