# Nonlinear Systems

1. Jun 5, 2009

### Stratosphere

1. The problem statement, all variables and given/known data
solve the system of $$3x^{2}+2y^{2}=35$$ and
$$4x^{2}-3y^{2}=24$$

2. Relevant equations

3. 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?

2. Jun 5, 2009

### 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?

3. Jun 5, 2009

### Stratosphere

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?

4. Jun 5, 2009

### HallsofIvy

Staff Emeritus
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.