# Simultaneous equation question

1. Oct 30, 2005

### james_rich

Hey just need my answer to be checked on this problem
just to clarify x2 means x squared!

Solve the following

y = 2 - x
x2 + 2xy = 3

Substitute equations

x2 + 2x(2 - x) = 3
x2 + 4x - 2 x2 = 3
-x2 + 4x - 3 = 0

Factorising

(-x + 1) (x - 3) = 0

so x = -1 and 3
_____________________________________________

as y = 2 - x

y = 2 - 3
= -1

y = 2 + 1
= 3

so the co ordinates for the two roots of this curve will be

(-1, 3) and (3, -1)

is this the right answer? i believe it to be, but my answer books says differently!

2. Oct 31, 2005

### roger

You made a small mistake where I highlighted.

3. Oct 31, 2005

### james_rich

sorry, i still don't understand, i checked what i did, i can't see whats wrong with the bit highlighted!

Can anyone elaborate?

4. Oct 31, 2005

### TD

I didn't read it all but if your factorization was correct, then x = 1 is a solution and not x = -1.

5. Oct 31, 2005

### james_rich

i think i see what i have done wrong

the x = 3 is right

but it is -x = -1!

so x = 1

so to start again............

as y = 2 - x
y = 2 - 3
= -1
y = 2 - 1
= 1
so the co ordinates for the two roots of this curve is
(-1, 3) and (1, 1)

Thanx a lot, this is the answer in the book, easy mistake i made i think! bah humbug with the positive and negative signs!!

Cheers! I can sleep now!

6. Oct 31, 2005

Good

7. Nov 1, 2005

### verty

A word of advice, when you factorise like that it usually helps to have the x^2 coefficient be positive.