SOLUTION: what is the point of intersection of the following systems of equations algebraically? xy=8 x+y=6

What is the point of intersection of the following 
systems of equations algebraically?

      xy = 8
   x + y = 6

Method: substitution.

Solve the second equation for y

       y = 6 - x

Substitute (6 - x) for y in the first equation

      xy = 8

x(6 - x) = 8

 6x - x² = 8

Get 0 on the left

       0 = x² - 6x + 8

       0 = (x - 2)(x - 4)

Use the zero-factor property

x - 2 = 0 gives x = 2

x - 4 = 0 gives x = 4

There are two values for x.

For each of these two values for x, we must
find a corresponding value for y.  We use

       y = 6 - x

To find the y-value that corresponds to x = 2

       y = 6 - 2

       y = 4

So one solution is the point (x, y) = (2, 4)

To find the y-value that corresponds to x = 4

       y = 6 - 4

       y = 2

So the other solution is the point (x, y) = (4, 2)

Edwin McCravy
AnlytcPhil@aol.com