Help with Simultaneous equation please

[curiosity]

I haven't done these for over 20 years. My daughter has managed her homework apart from one equation, which I've tried to work out. I'm frustrated as I used to be able to do these. Anyway I thought I had an answer but now Im totally confused can someone help:
xy = -4
2y = x + 6
I'd like to get my head around these so I can help her, so if you know the answer will you explain how you got to it please. Many thanks in advance.

[Aperio]

Substitute for one of the variables, say y.

y=-4/x; -8/x=x+6; Rearrange x*x +6x +8=0.

Factorise: (x+2)(x+4)=0 ; x=-2 or x=-4

x=-2 , y=2; x=-4, y=1.

[smouse]

y = -1 x = -4

[smouse]

sorry stuck a minus on my answer and someone has now given you second answer

[ageing fast]

I've come up with the answer x=-2 and y= 2.

If xy = -4, then one of x and y must be negative. The factors of 4 are limited to 1 x 4 or 2 x 2.

Then by trial, the second equation will only work using x=-2 and y=2.

The usual replacement technique for simultaneous equations won't work here because of the multiplication of x and y as in replacement this leads to squared symbols appearing.

It's late so I don't know if I've explained it very well!

[ageing fast]

Aperio's answer is spot on.

[curiosity]

Thanks ageing fast, your mention of the saured symbols matches what I was getting and hence confused. Is that why Aperio factorised? oh and Aperio thanks very much but what is factorising again?

[ageing fast]

Factorising is breaking down an equation as in Asperio's example:

x*x + 6x + 8 = 0 breaks down to

(x+2)(x+4) = 0

Then you know that one of the bracketed terms must be zero- so x = -2 or x =-4