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# core1 - point of intersection question

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1. 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?
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?
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.
3. (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 .
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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