Question 1169116

let the larger number be {{{x}}} and the smaller {{{y}}}

if their difference is {{{2}}} we have

{{{x-y=2}}}....solve for {{{x}}}

{{{x=y+2}}}......eq.1

 and if four times the smaller minus three times the larger is
{{{17}}}, we have 

{{{4y-3x=17}}}......solve for {{{x}}}

{{{4y-17=3x}}}

{{{x=(4y-17)/3}}}.....eq.2

from eq.1 and eq.2 we have

{{{y+2=(4y-17)/3}}}.....solve for {{{y}}}

{{{3y+6=4y-17}}}

{{{17+6=4y-3y}}}

{{{y=23}}}


go to 

{{{x=y+2}}}......eq.1, substitute {{{y}}}

{{{x=23+2}}}

{{{x=25}}}


so,  two numbers are {{{25}}} and {{{23}}}