the graphs of the equations xy=16 and y=x are drawn on the same set of axes. In which quadrant or quadrants will they intersect?

Given the curves:

xy
=16

Then we will rewrite as a function of
x.

==> y= 16/x
...........(1)

And the curve
:

y= x...............(2)

We
need to find the intersections points .

==> y=
y

==> x = 16/x

We will
multiply by x.

==> x^2 =
16

==> x = +-4

Then, we
have two intersection points at x1= 4 and x2= -4

Now we
will find the y-coordinate.

==> y1= x1=
4

==> y2= x2= -4

Then,
the points of intersection are :

(4,4) and
(-4,-4)

The point (4,4) is located in the
first quadrant and the point (-4,-4) is located in the third
quadrant.