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

Answer:

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.!