SOLUTION: The sum of two numbers is 38. Their difference is 10. What are the two numbers?

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Question 124657: The sum of two numbers is 38. Their difference is 10. What are the two numbers?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The sentence "The sum of two numbers is 38" translates to the equation x%2By=38



The sentence "Their difference is 10" translates to the equation x-y=10




Start with the given system of equations:

system%28x%2By=38%2Cx-y=10%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


y=%28-x%2B38%29%2F%281%29 Divide both sides by 1


y=%28%28-1%29%2F%281%29%29x%2B%2838%29%2F%281%29 Break up the fraction


y=-x%2B38 Reduce



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

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=10 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=10 Distribute the negative


2x-38=10 Combine like terms on the left side


2x=10%2B38Add 38 to both sides


2x=48 Combine like terms on the right side


x=%2848%29%2F%282%29 Divide both sides by 2 to isolate x



x=24 Divide





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


So the first part of our answer is: x=24









Since we know that x=24 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=-%2824%29%2B38 Plug in x=24


y=-24%2B38 Multiply


y=14 Combine like terms



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


So the second part of our answer is: y=14









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

So our answers are:

x=24 and y=14

which form the point




So the two numbers are 24 and 14