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core1 - point of intersection question

Find the co-ordinates of the point of intersection between the line y=5-x and the curve xy=-4.
so far , i substituted y=5-x into the equation xy=-4 to get: -x^2+5x+4=0
then i completed the square since i couldnt factorise that. and the x cordinate from the completing the square was 5/2. what do i do after this to find the points of intersection?
Original post by Chelsea12345
Find the co-ordinates of the point of intersection between the line y=5-x and the curve xy=-4.
so far , i substituted y=5-x into the equation xy=-4 to get: -x^2+5x+4=0
then i completed the square since i couldnt factorise that. and the x cordinate from the completing the square was 5/2. what do i do after this to find the points of intersection?


Firstly, there are two point of intersection so you need 2 x-coordinates that you get from solving the quadratic.

Secondly, you must've completed the square correctly, but you did not solve for x.

Thirdly, once you have the two x-coordinates, subtitute them into the line equation to get your y-values.
Reply 2
Original post by Chelsea12345
Find the co-ordinates of the point of intersection between the line y=5-x and the curve xy=-4.
so far , i substituted y=5-x into the equation xy=-4 to get: -x^2+5x+4=0
then i completed the square since i couldnt factorise that. and the x cordinate from the completing the square was 5/2. what do i do after this to find the points of intersection?


You should obtain the quadratic x25x4=0 x^2-5x-4=0 .
You should find the x coordinates and then sub these x values to find y to find the coordinates a of intersection.

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