Find all orders pairs (x, y) that satisfy the system:

Question

anonymous · Answer

$$x ^{3}-x ^{2}y+5xy ^{2}-y ^{3}=124$$

$$x ^{3}-5x ^{2}y+xy ^{2}-y ^{3}=4$$

hero · Answer

4x^2y + 4xy^2 = 120
4xy(x + y) = 120
xy(x + y) = 30

(x,y) = (3,2)
(x,y) = (2,3)

hero · Answer

@CrystalSkull

anonymous · Answer

How do you get that from xy(x+y)=30?

hero · Answer

Because once you get to that point it becomes this:

You know 6 x 5 = 30

Therefore make xy = 6 and (x + y) = 5

Now you're looking for two numbers that multiply to get 6 but add to get 5. 
You do that all the time when solving quadratic equations.

anonymous · Answer

k thanks

hero · Answer

What grade are you in?

anonymous · Answer

11th

hero · Answer

I see. Well, there could be another way to do it, but I'm pretty sure this is the easiest.

hero · Answer

I'd be interested in knowing what your teacher's solution is to this.

hero · Answer

To see if he or she does it differently

anonymous · Answer

I'll remember to post it if he ever goes over it.

hero · Answer

OK, deal. At the very least, just ask him for an alternative solution to the one you have.

hero · Answer

I'm really just interested in knowing if his is easier than mine. I doubt if it is.