SOLUTION: The sum of two numbers is 41 and their difference is 14. Find the numbers. not sure but 2 + x - 14 = 41

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Question 151389: The sum of two numbers is 41 and their difference is 14. Find the numbers.
not sure but 2 + x - 14 = 41
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The sum of two numbers is 41" translates to x%2By=41

and

"their difference is 14" translates to x-y=14


So we have the system of equations:

system%28x%2By=41%2Cx-y=14%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2By%29%2B%28x-y%29=%2841%29%2B%2814%29


%28x%2Bx%29%2B%28y-y%29=41%2B14 Group like terms.


2x%2B0y=55 Combine like terms. Notice how the y terms cancel out.


2x=55 Simplify.


x=%2855%29%2F%282%29 Divide both sides by 2 to isolate x.


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x%2By=41 Now go back to the first equation.


55%2F2%2By=41 Plug in x=55%2F2.


2%2855%2Fcross%282%29%2By%29=2%2841%29 Multiply both sides by the LCD 2 to clear any fractions.


55%2B2y=82 Distribute and multiply.


2y=82-55 Subtract 55 from both sides.


2y=27 Combine like terms on the right side.


y=%2827%29%2F%282%29 Divide both sides by 2 to isolate y.


So our answer is x=55%2F2 and y=27%2F2.


So the two numbers are 55%2F2 and 27%2F2