SOLUTION: The sum of two numbers is 14. The larger number is 2 more than 3 times the smaller number. Find the two numbers that satisfy these requirements. I don't really understand this

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: The sum of two numbers is 14. The larger number is 2 more than 3 times the smaller number. Find the two numbers that satisfy these requirements. I don't really understand this      Log On


   

Question 721027: The sum of two numbers is 14. The larger number is 2 more than 3 times the smaller number. Find the two numbers that satisfy these requirements.
I don't really understand this question.
PLEASE help me!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 14 ----> x+y = 14

Solve for y to get y = 14 - x

------------------------------------------------------------------

The larger number is 2 more than 3 times the smaller number ----> y = 3x + 2

Note: y is implied to be the larger number (in this case). You could easily make x the larger number (and it wouldn't change the final answer)
------------------------------------------------------------------

y = 3x + 2

14 - x = 3x + 2 ... plug in y = 14 - x (ie replace y with 14 - x)

-x=3x+2-14

-x-3x=2-14

-4x=2-14

-4x=-12

x=(-12)/(-4)

x=3

Now that you know x = 3, you can use it to find y

y = 14 - x

y = 14 - 3

y = 11

So the solutions are x = 3 and y = 11

Therefore, the two numbers are 3 and 11