# Thread: I need help with an eqvation system

1. ## I need help with an eqvation system

( 2 / ( x + y ) ) - ( 5 / ( x - y ) ) = -9
( 1 / ( x + y ) ) + (3 / ( x - y ) ) = 1

I'm so sorry but i can't type as you do, but can you try to understand it.

2. ## Re: I need help with an eqvation system

Put $\displaystyle \frac{1}{x+y}=A,\quadquad \frac{1}{x-y}=B,$

solve for $\displaystyle A$ and $\displaystyle B,$ and then solve for $\displaystyle x$ and $\displaystyle y.$

3. ## Re: I need help with an eqvation system

I tried that but didn't go far, can you explain more detailed on how to continue from there?

4. ## Re: I need help with an eqvation system

Making the indicated substitutions gets you the equations

$\displaystyle 2A-5B=-9,$
$\displaystyle A+3B=1.$

Solve these for $\displaystyle A$ and $\displaystyle B$ and then substitute into the earlier substitutions.

$\displaystyle x+y=1/A,$
$\displaystyle x-y=1/B.$

You should be able to solve both sets easily.

5. ## Re: I need help with an eqvation system

Oh thanks to you