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! :)
Jun 15

Jim J.