The larger of two numbers is 7 more than twice the smaller. if the smaller is subtracted from the larger, the result is 14. find the numbers.

To solve this problem, start by assigning a variable to your two numbers and using what you're told to write two equations involving those variables. Since you want to find two numbers, you'll have two variables, and you want two equations. (Remember that you need as many equations as you have variables to find the value of those variables!)

Let's call the larger number, a, and the smaller number, b.

Equation 1) You know that the larger number (a) is 7 more than twice the smaller number (b):
That means a = 2b (twice the smaller number) + 7 (seven more).

Equation 2) You know that if the smaller number (b) is subtracted from the larger number (a), the result is 14:
That means a - b = 14.

Now you have two equations a = 2b + 7 and a - b = 14, so you can solve for them using a system of equations.

To solve a system of equations, you can use substitution, elimination, or graphing. I will use substitution:
1) Start by solving one equation for a variable. I'll solve a - b = 14 for a, but you can solve for b or solve the other equation for either a or b:


2) Substitute the value of the variable you found from step 1 into the other equation, and solve for the value of the other variable:


3) From step 2, you know the value of one of the variables, b = 7. Substitute this value into either of your original equations to find the value of the other variable, a. I'll be substituting b = 7 into a - b = 14, but you can substitute it into a = 2b + 7:


The value of a = 21 and the value of b = 7.

That means your two numbers are 21 and 7.