Let x represent one number and let y represent the other number. Use the following conditions to write a system of nonlinear equations. Solve the system and find the numbers. The sum of two numbers is 17 and the product of the two numbers is 72. The two numbers are (Use a comma to separate answers as needed.)

Solution

L e t x re p rese n t o n e n u mb er an d l e t y re p rese n t t h e o t h er n u mb er . U se t h e f o ll o w in g co n d i t i o n s t o w r i t e a sys t e m o f n o n l in e a r e q u a t i o n s . S o l v e t h e sys t e m an d f in d t h e n u mb ers . T h e s u m o f tw o n u mb ers i s 17 an d t h e p ro d u c t o f t h e tw o n u mb ers i s 72. T h e tw o n u mb ers a re (U se a co mma t o se p a r a t e an s w ers a s n ee d e d .)

The numbers : 9, 8

Solution steps

Represent the numbers with

x and y

number 1 : x

number 2 : y

A.T.Q.:

x + y = 17

x y = 72

x + y = 17, x y = 72 : (x = 9, y = 8 x = 8, y = 9)

Discard duplicated solutions

The numbers : 9, 8