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

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

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

So we have the system of equations

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute the negative

Combine like terms on the left side

Subtract 1 from both sides

Combine like terms on the right side

Divide both sides by -1 to isolate x

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and

So our two numbers are -13, -27

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

So this verifies our answer

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

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