Question 202069
First, we need to translates the word problems into equations:


"The sum of two numbers is 2" translates to {{{x+y=2}}}



and "their difference is 26" means that {{{x-y=26}}}



Note: this implies that {{{x>y}}}





So we then get the system of equations:



{{{system(x+y=2,x-y=26)}}}



{{{x+y=2}}} Start with the first equation.



{{{y=2-x}}} Subtract {{{x}}} from both sides.



{{{y=-x+2}}} Rearrange the terms.



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{{{x-(-x+2)=26}}} Now plug in {{{y=-x+2}}} into the second equation.



{{{x+x-2=26}}} Distribute.



{{{2x-2=26}}} Combine like terms on the left side.



{{{2x=26+2}}} Add {{{2}}} to both sides.



{{{2x=28}}} Combine like terms on the right side.



{{{x=(28)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=14}}} Reduce.



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Since we know that {{{x=14}}}, we can use this to find {{{y}}}.



{{{x+y=2}}} Go back to the first equation.



{{{14+y=2}}} Plug in {{{x=14}}}.



{{{y=2-14}}} Subtract {{{14}}} from both sides.



{{{y=-12}}} Combine like terms on the right side.



So the solutions are {{{x=14}}} and {{{y=-12}}}.



This means that the two numbers are 14 and -12