SOLUTION: Difference of two numbers is 14. The second is less that 2 times the first. What are two numbers? > > I found a way for this to be both -13 and -27, or 15 and 29. Which is correc

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Difference of two numbers is 14. The second is less that 2 times the first. What are two numbers? > > I found a way for this to be both -13 and -27, or 15 and 29. Which is correc      Log On


   

Question 110668: Difference of two numbers is 14. The second is less that 2 times the first. What are two numbers?
>
> I found a way for this to be both -13 and -27, or 15 and 29. Which is correct?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=first number, y=second number


So the difference of two numbers is x-y=14 (simply subtract the two to get 14). Also, since the "second is less that 2 times the first", this means y=2x-1


So we have the system of equations
x-y=14
y=2x-1






x-%282x-1%29=14 Plug in y=2x-1 into the first equation. In other words, replace each y with 2x-1. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


x-2x%2B1=14 Distribute the negative


-x%2B1=14 Combine like terms on the left side


-x=14-1Subtract 1 from both sides


-x=13 Combine like terms on the right side


x=%2813%29%2F%28-1%29 Divide both sides by -1 to isolate x



x=-13 Divide




Now that we know that x=-13, we can plug this into y=2x-1 to find y



y=2%28-13%29-1 Substitute -13 for each x


y=-27 Simplify


So our answer is x=-13 and y=-27


So our two numbers are -13, -27


Check: Notice if we subtract -27 from -13, we get

-13--27=-13%2B27=14

So this verifies our answer


note: with your other answer 15,29, if you subtract, you get:
15-29=-14 which is not what we want