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

• Sep 13th 2012, 06:25 AM
niktoo1
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?
• Sep 13th 2012, 06:41 AM
MarkFL
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?
• Sep 13th 2012, 06:59 AM
BobBali
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! :-)
• Sep 13th 2012, 07:08 AM
Wilmer
Re: I'm struggling to solve this strange simultaneous equation. Can someone help me?
Quote:

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
• Sep 15th 2012, 09:42 PM
niktoo1
Re: I'm struggling to solve this strange simultaneous equation. Can someone help me?
Quote:

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 :)