Thread: How to solve this system of equations?

1. How to solve this system of equations?

I have never solved any system consisting of squared numbers. I have been trying to figure this one out now for a while without any luck.

x^2 - y^2 = -(15/4)
2xy = 2

Basically, what I would like to do is
2xy = 2 <=> xy = 1 <=> x = 1 / y
then insert that into the top equation, but doing so will give me a new grade four equation, which cannot be right?

2. Originally Posted by Sabo
I have never solved any system consisting of squared numbers. I have been trying to figure this one out now for a while without any luck.

x^2 - y^2 = -(15/4)
2xy = 2

Basically, what I would like to do is
2xy = 2 <=> xy = 1 <=> x = 1 / y
then insert that into the top equation, but doing so will give me a new grade four equation, which cannot be right?
$\displaystyle \frac{1}{y^2} - y^2 = -\frac{15}{4}$

multiply every term by $\displaystyle 4y^2$ ...

$\displaystyle 4 - 4y^4 = -15y^2$

$\displaystyle 0 = 4y^4 - 15y^2 - 4$

$\displaystyle 0 = (4y^2 + 1)(y^2 - 4)$

finish up.