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

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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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
If "The sum of two numbers is 38", then the first equation is x%2By=38



If "Their difference is 12", then the second equation is x-y=12



So we have the system:


system%28x%2By=38%2Cx-y=12%29



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

x%2By=38 Start with the first equation


y=38-x Subtract x from both sides


y=-x%2B38 Rearrange the equation




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

Since y=-x%2B38, we can now replace each y in the second equation with -x%2B38 to solve for x



x-highlight%28%28-x%2B38%29%29=12 Plug in y=-x%2B38 into the first equation. In other words, replace each y with -x%2B38. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2Bx-38=12 Distribute the negative


2x-38=12 Combine like terms on the left side


2x=12%2B38Add 38 to both sides


2x=50 Combine like terms on the right side


x=%2850%29%2F%282%29 Divide both sides by 2 to isolate x



x=25 Divide





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


So the first part of our answer is: x=25









Since we know that x=25 we can plug it into the equation y=-x%2B38 (remember we previously solved for y in the first equation).



y=-x%2B38 Start with the equation where y was previously isolated.


y=-%2825%29%2B38 Plug in x=25


y=-25%2B38 Multiply


y=13 Combine like terms



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


So the second part of our answer is: y=13









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

So our answers are:

x=25 and y=13



Answer:


So the two numbers are 25 and 13