Intersection of a line and curve.

RickyOswaldIOW · 2007-01-25 08:40:02

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?

luca-deltodesco · 2007-01-25 08:42:09

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

RickyOswaldIOW · 2007-01-25 08:44:43

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

luca-deltodesco · 2007-01-25 08:47:16

or you could equally, substitute 4/y into the first equation, and end up with a quadratic in y 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

Stanley_Marsh · 2007-01-26 10:22:29

Eliminate the x or y and solve the equation

Math Is Fun Forum

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

Intersection of a line and curve.

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

Re: Intersection of a line and curve.

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

Re: Intersection of a line and curve.

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

Re: Intersection of a line and curve.

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

Re: Intersection of a line and curve.

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