If xy = 144, x + y = 30, and x > y, what is the value of x – y ?

Given the equations:

x*y =
144.............(1)

x+ y= 30
.............(2)

We will use the substitution method to
find the values of x and y.

from (2) we know that y=
30-x

Now we will substitute into
(1).

==> x*y=
144

==> x*(30-x) =
144

Now we will open the
brackets.

==> 30x - x^2 =
144

==> x^2 - 30x + 144 =
0

Now we will
factor.

==> (x -24) ( x-6)  =
0

==> x1= 24 ==> y1= 30-24
=6

==> x2= 6==> y2= 30-6 =
24

But we know that
x>y

Then the values are : x= 24 and y=
6

Now we need to find the values of
x-y

==> x-y = 24-6 =
18