Set up a system of linear equations, and then solve for the indicated quantities.Four times the smaller of two numbers plus five times the larger number is-13 .Five times the smaller number minus five times the larger number is-5 .Find the numbers.Let x represent the smaller number. Let represent the larger number.

Solution

S e t u p a sys t e m o f l in e a r e q u a t i o n s, an d t h e n so l v e f or t h e in d i c a t e d q u an t i t i es . F o u r t im es t h e s ma ll er o f tw o n u mb ers pl u s f i v e t im es t h e l a r g er n u mb er i s - 13 . F i v e t im es t h e s ma ll er n u mb er min u s f i v e t im es t h e l a r g er n u mb er i s - 5 . F in d t h e n u mb ers . L e t x re p rese n t t h e s ma ll er n u mb er . L e t re p rese n t t h e l a r g er n u mb er .

The numbers : - 2, - 1

Solution steps

Represent the numbers with

x and y

number 1 : x

number 2 : y

A.T.Q.:

4 x + 5 y = - 13

5 x - 5 y = - 5

4 x + 5 y = - 13, 5 x - 5 y = - 5 : x = - 2, y = - 1

The numbers : - 2, - 1