Find the points of intersection of the curve xy=6 and the the line y=9-3x

To find the points of intersection of the curve xy =6 and
the line y =
9-3x,

Solution:

xy =
6......(1)

y =
9-3x................(2).

We eliminate y between xy = 6 and 
y = 9-3x by substituting y = 9-3x fot y in xy=6.

x(9-3x) =
6.

9x-3x^2= 6

9x-3x^2 -6 =
0

Multiply by (-1):

3x^2 -9x +
6 = 0

Divide by 3:

x^2-3x+2 =
0

(x-1)(x-2) = 0

x-1 = 0. Or
x-2 = 0

x = 1 . Or x = 2.

To
get corresponding y values, put x= 1  in xy = 6: 1*y = 6. Or y =
6.

Put x= 2 in xy =6: 2*y = 6. So y = 6/2 =
3.

Therefore (x,y) = (1,6) or (x,y) = (2,3) are the point
of intersection of the curve xy = 6 and y =  9-3x.