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find the points of intersection between a line and a curve algebraically?

i have this question on my add maths fmsq homework
i've seen stuff like this before but i don't have a clue how to solve it.
can anyone help?
its question 9 on this sheet

many thanks
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Use simultaneous equations.
Use simultaneous equations.
It is the best method to find point of intersection.
Reply 3
Avatar for TSR George
TSR George
OP
17
Original post by kundanad
Use simultaneous equations.
It is the best method to find point of intersection.

I understand that i should sue simultaneous equations to solve it but i don't know how to do the simultaneous equation. can you help me out a bit?
A more easier way to visualise it is to think of them as when are the values of both functions the same, as that is what it means for them to intersect. So you rearrange equation 1 so you get a function in terms of x, so y=-3x-3 and you equate them both and solve for x and then you'll plug the solutions in to find the value and there are your points.

Original post by kundanad
Use simultaneous equations.
It is the best method to find point of intersection.

The guy is asking for more help and you literally just say the same thing the first poster said, genius...
You can substitute the value of y.
x^2-5x-3+3x+3=0 and then simplify and solve.
you should get the value of x and then y.
I hope that helped :smile:
(edited 4 years ago)
Make y the subject for both equations and equate them.
Reply 7
Avatar for Loci Pi
Loci Pi
16
1. Put the first equation in the form where y is the subject.
2. Make the equations equal to each other.
3. Put in the form ax^2 + bx + c = 0.
4. Solve your quadratic to find the values of x.
5. Substitute them into one of the equations to find y.
6. Write out the co-ordinates of the points of intersection.
(edited 4 years ago)
Reply 8
Avatar for Loci Pi
Loci Pi
16
No problem :smile:
Reply 9
Avatar for MR1999
MR1999
21
Just a tip you should keep in mind: sometimes they'll give you a point of intersection or they'll make that point impossible, by making it outside of the valid range of x values. So when you give your answer, you should be careful to select the correct point, otherwise, you could lose a mark or two.

Just to illustrate my point, you may find two points P(1,2),Q(10,11) P(1,2), Q(10,11), but the function was defined f(x),x>1 f(x), x > 1 . So if you put P as an answer, you would lose a mark, or maybe even two.
(edited 6 years ago)

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