Question 202005
"the sum of two numbers is 16" translates to {{{x+y=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(x+y=16,2x-y=20)}}}



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



{{{(x+y)+(2x-1y)=(16)+(20)}}}



{{{(1x+2x)+(1y+-1y)=16+20}}} Group like terms.



{{{3x+0y=36}}} Combine like terms.



{{{3x=36}}} Simplify.



{{{x=(36)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=12}}} Reduce.



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{{{x+y=16}}} Now go back to the first equation.



{{{12+y=16}}} Plug in {{{x=12}}}.



{{{12+y=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.