**Quote:**

*y*² = 4 and *y* = 2

Note that each equation like this one yields two solutions:

*y* = 2 and

*y* = -2 .

But more important here is the following:

questioner wrote:

(2) *xy* = 2 . Define *x* in terms of *y*: *x* = *y*/2

*xy* = 2 implies

*x* = 2/

*y*.

So the equation (1) becomes

(2/

*y*)² +

*y*² = 5

4/

*y*² +

*y*² = 5

4 + (

*y*²)² = 5

*y*²

(

*y*²)² – 5

*y*² + 4 = 0

(

*y*² – 1)(

*y*² – 4) = 0

*y*² = 1 or

*y*² = 4

This yields the four possible solutions: -2, -1, 1, 2 .

When you calculate

*x*, you'll see that

*x* +

*y* can be -3 or 3 .