1. [SOLVED] solving a system

Can someone point me in the right direction to solve this system of equations?

$\displaystyle x^2 + y^2 = 25$
$\displaystyle 3x^2 - 16y = 0$

I'm trying to use substitution to get the answer. However, regardless of which direction I go, the answers get hopelessly convoluted. Can someone point me at how to start?

2. Originally Posted by satis
Can someone point me in the right direction to solve this system of equations?

$\displaystyle x^2 + y^2 = 25$
$\displaystyle 3x^2 - 16y = 0$

I'm trying to use substitution to get the answer. However, regardless of which direction I go, the answers get hopelessly convoluted. Can someone point me at how to start?
$\displaystyle x^2 = 25 - y^2$

$\displaystyle 3(25-y^2) - 16y = 0$

$\displaystyle 75 - 3y^2 - 16y = 0$

$\displaystyle 3y^2 + 16y - 75 = 0$

$\displaystyle (3y+25)(y-3) = 0$

$\displaystyle y = -\frac{25}{3}$

$\displaystyle y = 3$

$\displaystyle x^2 = 25 - \left(-\frac{25}{3}\right)^2 = -\frac{400}{9}$
no solution for x in this equation. this y-value is invalid.

$\displaystyle x^2 = 25 - 9 = 16$

$\displaystyle x = \pm 4$

so, two solutions ... (4,3) and (-4,3)

3. excellent, thank you, that was precisely what I needed.