The sum of two integers is 19 and their difference is 10. what is the smaller of the two integers?

need two variables and two equations. it also needs to be solved.

You an make a system of equations. lets make a the smaller number and b the larger number.  The first equation is b+a=19 and the second equation is b-a=10.  we know the second equation has to be the larger number minus the smaller number since the differece is a positive number.  Know that we have the two equation made the fallowing system of equations:
b+a=19 (add the bottom equation to the top equation)
b-a=10  (b+b=2b, a-a=0, and 19+10=29)
Since the a got canceled out, you can write one equation 2b=29 which means b=29/2.  a=19-(29/2) (by plugging the value for b into the equation b+a=19 and solving for a) which means a=9/2.
Since we are looking for the smaller number the answer is 9/2

I hope this helps.