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

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The sentence "The sum of two numbers is 38" translates to the equation



The sentence "Their difference is 10" translates to the equation




Start with the given system of equations:





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


Divide both sides by


Break up the fraction


Reduce



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

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

which form the point




So the two numbers are 24 and 14