SOLUTION: the sum of two numbers is 16 when the small number is subtracted from two times the larger number the difference is 20 what are the two numbers

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Question 202005: the sum of two numbers is 16 when the small number is subtracted from two times the larger number the difference is 20 what are the two numbers
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"the sum of two numbers is 16" translates to x%2By=16


"the small number is subtracted from two times the larger number the difference is 20" translates to 2x-y=20





Start with the given system of equations:
system%28x%2By=16%2C2x-y=20%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%282x-1y%29=%2816%29%2B%2820%29


%281x%2B2x%29%2B%281y%2B-1y%29=16%2B20 Group like terms.


3x%2B0y=36 Combine like terms.


3x=36 Simplify.


x=%2836%29%2F%283%29 Divide both sides by 3 to isolate x.


x=12 Reduce.


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x%2By=16 Now go back to the first equation.


12%2By=16 Plug in x=12.


12%2By=16 Multiply.


y=16-12 Subtract 12 from both sides.


y=4 Combine like terms on the right side.


So the solutions are x=12 and y=4.


This means that the larger number is 12 and the smaller number is 4.