Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Simultaneous Equations

Sorry, another one! I'm going over past papers, you see.

Solve the simultaneous equations:

I did the following:

I don't see what is wrong with this, but my teacher has done a big red cross next to it all???

thanks.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Simultaneous Equations

It was a bit mean of your teacher to just mark it all wrong, but I think the reason is that your working actually just gets you to another set of simultaneous equations, and then you just give the answers without solving them. It's fairly easy to solve them from there, you just didn't.

xy = 2; x = 2y
∴ 2y² = 2
y² = 1
y = ± 1
y=1 ⇒ x=2; y=-1⇒x=-2
∴ (2,1), (-2,-1)

I like how you've extended the method for solving linear simultaneous equations, but the more common method here is substitution.

You're given that x=2y, and so plugging that into the second given equation produces:
(2y)² + 3x(2y) = 10, which is a quadratic with one variable that you can simplify and solve, and then use the answers to find x.

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Why did the vector cross the road?
It wanted to be normal.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Simultaneous Equations

Oohh.. thanks mathsy!