two numbers have a sum of 24, and 7 times the first number minus the second number is equal to 16. what is the smallest number?

i'm supposed to translate the word problem into a system of equations then solve. please help!!

let x and y be the 2 numbers.
 
solve this system of equations:
 
x + y = 24
7x - y = 16
 
add the 2 equations and get
 
8x = 40
x = 40/8 = 5
 
y = 24 - 5 = 19
 
the 2 numbers are 5 and 19.  test the answers.
 
 

hi niya,
 
let's call the two numbers a and b. 
 
now, lets' read the problem word for word and convert it to math symbols:
"the sum of the numbers is 24" which means
 
a + b = 24  (this is the first equation of your system)
 
next, we read, "7 times the first number minus the second number is equal to 16" which means
7a - b = 16  (this is the second equation of your system)
 
 
if i take the first equation and solve it for b (which means get b by itself on one side), we see that
b = 24 - a
 
let's use this expression for b and substitute it in for b in the second equation
7a - b = 16
7a - (24 - a) = 16     see the replacement!  :)
 
7a - 24 + a = 16      distribute the negative on the left side)
 
8a - 24 = 16
 
8a = 16 + 24
 
8a = 40
 
a = 5
 
which means that b must be 19 since the two numbers have to add up to 24.
 
a is the smallest number!  a = 5
 
hope this helps!  :)