# The sum of two numbers is 19. The sum of twice the smaller number and thrice the larger number is 48. What are the two numbers?(Enter your answers in ascending order.)

2
by teriyaki

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by teriyaki

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y be the larger number

x+y=19 ----equation 1

2x+3y=48 -----equation 2

from eqn 1

x + y = 19

x = 19 - y -----equation 3

substitute equation 3 to equation 2

2(19-y)+3y = 48

38 - 2y + 3y = 48

y = 48 - 38

y = 10

substitute to equation 1

x + y =19

x + 10 = 19

x = 19 - 10

x = 9

so the numbers are 9 & 10

2x+ 3y= 48

2x=(48-3y)/2

x=24-3/2y

x+y=19

(24-3/2y)+ y= 19

24+1/2y=19

1/2y= -5/ (1/2)

y= -10

x+y=19

x+(-10)=19

x-10=19

x=29

-10 and 29?