1 Solve the system 2x y 5 x y 13 2 Bobby is three years

1. Solve the system: 2x + y = 5
x – y = 13

2. Bobby is three years older than twice Arianna’s age. If the total of their ages is 9, how old is Bobby, and how old is Arianna?

3. Solve the system: y = x² + 5
6x – y = 3

1) Consider the given system

2x + y = 5 ----------- ( 1 )

x - y = 13 -------------( 2 )

addind ( 1 ) and ( 2 ) we get, 3x = 18 implies that x = 6

and from equation ( 2 ) , y = 6 - 13 = - 7

There fore the solution of the system is x = 6 and y = - 7

2) Let the Arianna\'s age = x years

Then the age of Bobby = 2x+3

The sum of their age is x + (2x + 3 ) = 9

3x + 3 = 9 implies that x = 2

Therefore, the age of Arianna is 2 years and the age of Bobby is 7

3) Consider the given system

y = x² + 5 --------- ( 1 )

6x - y = 3 implies y = 6x - 3 ------------- ( 2 )

from ( 1 ) and ( 2 ) we have x² + 5 = 6x - 3

x² - 6x + 8 = 0

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

x = 4 or x = 2 and the values of y are y = 21 and y = 9

Therefore, the solution of the system are ( 4 , 21) and ( 2 , 9)