SOLUTION: the sum of two numbers is twelve. the square of the smaller is subtracted from the product the result is ten.Find the numbers

Question 523463: the sum of two numbers is twelve. the square of the smaller is subtracted from the product the result is ten.Find the numbers
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
x + y = 12
so
x = 12-y
.
x*y - x^2 = 10
so
x*y = x^2 +10
y = x + 10/x
.
substitute for x
.
(12-y)*y -(12-y)^2 = 10
.
12y -y^2 - ( (12-y)(12-y) ) = 10
.
12y - y^2 -144 +24y - y^2 = 10
.
-2y^2 +36y -144 = 10
.
-2y^2 +36y -154 = 0
.
y^2 -18y + 77 = 0
.
(y-7)(y-11) = 0
.
So
y = 7 or 11
.
x + y = 12
so
If y =7, x = 5
If y = 11, x = 1
.
Using ordered pair (x,y) notation, the solutions are: (1,11) and (5,7).
.
In the following graph:
red line is y = -x+12
green line is y = x + 10/x
.

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