How do you determine algebraically the x coordinate of all points where the graphs of xy=10 and y= x+3 intersect?

1 Answer
Sep 4, 2016

the desired x-co-ords. are -5,2.

Explanation:

To find algebraically the points of intersection of the given two

curves, we solve their eqns.

xy=10, and, y=x+3

rArr x(x+3)=10

rArr x^2+3x-10=0

rArrul(x^2+5x)-ul(2x-10)=0

rArr x(x+5)-2(x+5)=0

rArr (x+5)(x-2)=0

rArr x=-5, x=2

Since, y=x+3, the corresponding y=-2, y=5, resp.

Thus, the pts. of intersection are (-5,-2), (2,5)

These satisfy the given eqns.

Hence, the desired x-co-ords. are -5,2, as Respected brian gerard hart has derived (graphically).

Enjoy Maths.!