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.