# Thread: I'm struggling to solve this strange simultaneous equation. Can someone help me?

1. ## I'm struggling to solve this strange simultaneous equation. Can someone help me?

Solve the pair of simultaneous equations:
x+y=2xy
x-y=xy

I solved it to get x=2 and y=0.66
but the answer booklet says it is wrong?

2. ## Re: I'm struggling to solve this strange simultaneous equation. Can someone help me?

I get (x,y) = (2,2/3) or (0,0). What does your booklet gives as the solution?

3. ## Re: I'm struggling to solve this strange simultaneous equation. Can someone help me?

You have two equations: 1) x+y = 2xy 2) x-y =xy

In the first equation make y the subject. This gives you your third equation 3) y = 2xy-x > simplify > y = x(2y-1)

Sustitute this 3rd equation into the 2nd equation and solve it simultaneously.

I get x = 2x(2y-1) and y = -2x(y-1) Hope this helps! :-)

4. ## Re: I'm struggling to solve this strange simultaneous equation. Can someone help me?

Originally Posted by BobBali
You have two equations: 1) x+y = 2xy 2) x-y =xy
In the first equation make y the subject. This gives you your third equation 3) y = 2xy-x > simplify > y = x(2y-1)
Sustitute this 3rd equation into the 2nd equation and solve it simultaneously.
I get x = 2x(2y-1) and y = -2x(y-1) Hope this helps! :-)
Keep it simple:
x+y=2xy
x-y=xy
Simply add the equations together: 2x = 3xy ; 2 = 3y ; y = 2/3

5. ## Re: I'm struggling to solve this strange simultaneous equation. Can someone help me?

Originally Posted by MarkFL2
I get (x,y) = (2,2/3) or (0,0). What does your booklet gives as the solution?
Sorry guys there was a mistake in the answer booklet.
x=2
y=0.66 is correct