SOLUTION: The sum of two numbers is 38. Their difference is 12. What are the two numbers? the answer is 2x=50 that is right i know the answer but i dont know how to set the problem pro

Question 122873: The sum of two numbers is 38. Their difference is 12. What are the two numbers? the answer is 2x=50 that is right
i know the answer but i dont know how to set the problem problem up can some one show me
Found 2 solutions by checkley71, jim_thompson5910:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
YOU ARE HALF RIGHT. WHAT'S THE ANSWER FOR Y?
---------------------------
X+Y=38 OR X=38-Y
X-Y=12
NOW REPLACE X IN THE SECOND EQUATION BY (38-Y)
(38-Y)-Y=12
38-2Y=12
-2Y=12-38
-2Y=-26
Y=-26/-2
Y=13 ANSWER.
X+13=38
X=38-13
X=25 ANSWER.
PROOF
25-13=12
12=12

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If "The sum of two numbers is 38", then the first equation is

If "Their difference is 12", then the second equation is

So we have the system:

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

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

Since , we can now replace each in the second equation with to solve for

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

Add 38 to both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

Answer:

So the two numbers are 25 and 13

RELATED QUESTIONS
The sum of two numbers is 38. Their difference is 12. What are the two... (answered by ptaylor)
The sum of two numbers is 38. Their difference is 10. What are the two numbers? (answered by jim_thompson5910)
The sum of two numbers is 38. Their difference is 10. What are the two numbers? (answered by gems)
The sum of two numbers is 312. Their difference is 38. What are the two... (answered by Cromlix)
The sum of two numbers is 52 . Their difference is 38 . What are the two numbers ? (answered by Alan3354)
The sum of two numbers is 36. their difference is 12. What are the two... (answered by elima)
The sum of two numbers is -44. Their difference is 12. What are the two... (answered by anand429)
the sum of two numbers is 80 their difference is 12. what are the numbers (answered by fractalier)
The sum of two whole numbers is 112. Their difference is 12. What are the numbers? (answered by richwmiller)