please help solve this simutaneous equation

[divine]

Hi

I'm stumped with how to deal with this problem:

Solve the following system of equations

x + y = -1

1/x + 1/y = 1/2


Please help.

 

[stapel]

Since this is a non-linear equation, many of the usual techniques won't work. So you're pretty much looking at working by substitution.

I don't know about you, but I'd prefer not to have to work with fractions any more than I have to. So the first thing I would recommend doing is multiplying that second equation through by the common denominator, giving you the following equivalent (but re-arranged) system:

. . . . .x + y = -1

. . . . .2y + 2x = xy

Now solve the first equation for either one of the variables, and substitute the result into the second equation. This will give you a quadratic, which you can solve by factoring or by the Quadratic Formula.

Then plug the two solutions back into the first equation, and solve for the corresponding values of the other variable.

If you get stuck, please reply showing how far you've gotten. Thank you.

Eliz.

 

[divine]

simultaneous equation

Eliz.

Thanks very much for your reply.

I worked through the quadratic which gave me y=-2 or y=1.

Putting that back into the first equation gave me x = 1 when y =-2
and x = -2 when y = 1.


Thank you again for your help.

Div.