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#1 2007-01-25 08:40:02

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Intersection of a line and curve.

Hello all!  I've got a small problem here, I have to find the intersection of a line and curve, I can do this just fine on most of the questions but I'm having difficulty on this one:

2x + 3y = 14 meets xy = 4

Obviously I have to re-arrange the first to get y = 14/3 - 2/3x,  it is the second that I am having difficulty with.

How do I re-arrange xy = 4 to be a quadratic equation?  Since I didn't take my GCSE maths and went straight on to Advanced level, there are some gaps in my knowledge so if you could explain how I can re-arrange this and other similar equations it'd be much appreciated!

So far I've taken it to the step: y = 4/x

Am I on the right track?


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#2 2007-01-25 08:42:09

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Intersection of a line and curve.

i'd just do it like this:

xy = 4
y = 4/x

2x + 3(4/x) = 14
2x + 12/x = 14
2x^2 + 12 = 14x

2x^2 - 14x + 12 = 0


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#3 2007-01-25 08:44:43

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Re: Intersection of a line and curve.

Aha! So I just substitute the value of y into the first equation?  Thankyou luca smile


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#4 2007-01-25 08:47:16

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Intersection of a line and curve.

or you could equally, substitute 4/y into the first equation, and end up with a quadratic in y tongue either way is suitable, i chose to substitue the second equation into the first, as the second equation is a simpler one, so leads to a simpler substitution


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#5 2007-01-26 10:22:29

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: Intersection of a line and curve.

Eliminate the x or y and solve the equation


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