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AS Maths: Finding Coordinates from Simultaneous Equations

Hi there, im quite stuck on the following question:
"Find the coordinates of the points of intersection of the given straight lines with the given curves"

y=2x-12 x^2+4xy-3y^2= -27

I would like to know how to do it please as im rather confused on this topic!

Thanks! :biggrin:

(edited 13 years ago)

Reply 1

Mr M

Study Forum Helper

I think you need to give us the whole question.

Reply 2

~Sparked~

That is it above! Lol.

The bold is one equation, the non bold is the other.

Reply 3

nuodai

At the points of intersection, the x- and y-coordinates of the two curves must be equal, which means we can substitute one curve into the other. Since we know that

y=2x-12

on the first curve, it seems easiest to sub the y-coordinate of this curve into the equation of the second curve. This gives:

x^2+4x(2x-12) - 3(2x-12)^2 = -27

You can then expand and solve this to get the x-coordinates of the points of intersection. The y-coordinates can then be found by substituting the values of the x-coordinates into the first equation.