Question 178510
"The sum of two numbers is 45." translates to {{{x+y=45}}} 


and 


"Their difference is 9" translates to {{{x-y=9}}}




So we have the system of equations:

{{{system(x+y=45,x-y=9)}}}



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)+(x-y)=(45)+(9)}}}



{{{(x+x)+(y-y)=45+9}}} Group like terms.



{{{2x+0y=54}}} Combine like terms.



{{{2x=54}}} Simplify.



{{{x=(54)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=27}}} Reduce.



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{{{x+y=45}}} Now go back to the first equation.



{{{27+y=45}}} Plug in {{{x=27}}}.



{{{27+y=45}}} Multiply.



{{{y=45-27}}} Subtract {{{27}}} from both sides.



{{{y=18}}} Combine like terms on the right side.



So the answers are {{{x=27}}} and {{{y=18}}}.



This means that the two numbers are 27 and 18