Solving Nonlinear System: 3x2+2y2=35, 4x2-3y2=24

[Stratosphere]

Homework Statement

solve the system of $$3x^{2}+2y^{2}=35$$ and
$$4x^{2}-3y^{2}=24$$

Homework Equations

The Attempt at a Solution

I re arranged for y^2 and got $$1\frac{1}{3}x^{2}-16=y^{2}$$ I keep getting x to equal \pm 2.473 this is clearly wrong, the answers should be (–3, –2), (–3, 2), (3, –2), and (3, 2). What am I doing wrong?

 

[rock.freak667]

Instead of messing with fractions, why not just multiply the first equation by 3, the second equation by 2 and then just add them?

 

[Stratosphere]

Instead of messing with fractions, why not just multiply the first equation by 3, the second equation by 2 and then just add them?

Thanks for the help but I still have a question, after I combined the two equations how come it worked and it didn’t work when I rearranged them. Did I mess up?

 

[HallsofIvy]

Looks like a basic arithmetic error. Because of the "$1\frac{1}{3}$", which would better be left 4/3, it looks like you solved the second equation for y²: $3y^2= 4x^2- 24$ so $y^2= (4/3)x^2- 8$. 24/3= 8, not 16.