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Three times a number minus two times another number equals 19. The sum of the two number is 18. find the two numbers
 
Let m = one of the numbers and n = the other number
 
We have two unknowns (n and m), so we need two equations relating them to find the solution.
 
Equation 1 - Three times a number minus two times another number equals 19
 
3m - 2n = 19
 
Equation 2 - The sum of the two numbers is 18
 
m + n = 18
 
We can re-write this equation as:
 
n = 18 - m
 
Now let's substitute 18-m in place of n in Equation 1:
 
3m - 2n = 19             (equation 1)
 
3m - 2(18-m) = 19     (Substitute 18-m in place of n)
 
3m - 36 +2m = 19     (Multiply out the parentheses)
 
5m = 55                    (Add the m terms, add 36 to both sides)
 
Solve for m, then use n = 18 - m to solve for n.  Check your answers by putting them into equation 1 and verifying that they produce 19 for the answer.

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