Question 764774
let the greater number be {{{x}}} and the smaller number be {{{y}}}

if the sum is {{{83}}}, then  {{{x+y=83}}}.....eq.1

and if the difference of the two numbers is {{{41}}},then {{{x-y=41}}}.....eq.2


to find the smaller number, solve the system:

{{{x+y=83}}}.....eq.1
{{{x-y=41}}}.....eq.2
___________________________

{{{x+y=83}}}.....eq.1....solve for {{{x}}}

{{{x=83-y}}}.....plug it in eq.2

{{{83-y-y=41}}}.....eq.2....solve for {{{y}}}

{{{83-2y=41}}}
{{{83-41=2y}}}
{{{42=2y}}}
{{{42/2=y}}}
{{{highlight(21=y)}}}....so, the smaller number is {{{highlight(21)}}}

now we can find greater number {{{x}}}

{{{x=83-21}}}

{{{highlight(x=62)}}}....the greater number is {{{highlight(62)}}}