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

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.

$x y = 10 , \mathmr{and} , y = x + 3$

$\Rightarrow x \left(x + 3\right) = 10$

$\Rightarrow {x}^{2} + 3 x - 10 = 0$

$\Rightarrow \underline{{x}^{2} + 5 x} - \underline{2 x - 10} = 0$

$\Rightarrow x \left(x + 5\right) - 2 \left(x + 5\right) = 0$

$\Rightarrow \left(x + 5\right) \left(x - 2\right) = 0$

$\Rightarrow x = - 5 , x = 2$

Since, $y = x + 3 , t h e c \mathmr{and} r e s p o n \mathrm{di} n g y = - 2 , y = 5 , r e s p .$

Thus, the pts. of intersection are $\left(- 5 , - 2\right) , \left(2 , 5\right)$

These satisfy the given eqns.

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

Enjoy Maths.!