Question 706803

let numbers be {{{x}}} and {{{y}}}

if the sum of two numbers is {{{19}}}, we have {{{x+y=19}}}..eq.1


if their difference is {{{5}}}, we have {{{x-y=5}}}.....eq.2

to find the number, solve this system:

{{{x+y=19}}}..eq.1

{{{x-y=5}}}.....eq.2
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{{{x+y=19}}}..eq.1..solve for {{{x}}}

{{{x=19-y}}}....eq.1a....substitute in eq.2


{{{19-y-y=5}}}.....eq.2...solve for {{{y}}}

{{{19-2y=5}}}


{{{19-5=2y}}}

{{{14=2y}}}

{{{14/2=y}}}

{{{7=y}}} or

{{{highlight(y=7)}}} 


go back to eq. 1a and find {{{x}}}

{{{x=19-y}}}....eq.1a

{{{x=19-7}}}

{{{highlight(x=12)}}}