Determine the number of solutions to the following system.

xy = 2
x^2 = 3 + y^2

Question

Determine the number of solutions to the following system.

xy = 2
x^2 = 3 + y^2

anonymous · Answer

In order to tackle this problem, you want both equations to equal y. Always keep this in mind.

So, the first one could be changed to let y be by itself by dividing both sides by x,
so it becomes $$y=2/x$$

Then for the next one, the 3 has to be subtracted from both sides, and then the square root has to be taken of both sides, resulting in
$$y=\sqrt{2x-3}$$

Since this proves that both of these equation represent y, they both must be equal to each other. So set them equal to each other!
$$\sqrt{2x-3}=2/x$$

Bring all the terms together, set it equal to 0, and solve for x!

Simple enough. :)

anonymous · Answer

can you walk me thru that last step? how do you bring all the terms together?

anonymous · Answer

When you do AC Method, in a regular quadratic, its like this
$$ax^2+ax+a$$,
So you try to find factors such that multiply to get a but add to get ax. Check out the drawing.|dw:1341473645111:dw|
The ones that I underlined, that's the kinda thing you have to do, especially towards the end as well.