Question 633493
remember: An integer is a whole number (not a fraction) that can be positive, negative, or zero. 


let’s integers be {{{x}}} and {{{y}}}......the lesser integer, our integer is {{{x}}}
and  the greater integer is {{{y}}}
given:

{{{x+6=y}}}............1
if the product of the lesser integer {{{x}}} and {{{-7 }}}is {{{42}}} more 
than the greater integer {{{y}}}, than we have

{{{x(-7)=y+42}}}........2

solve this system
{{{x+6=y}}}............1....substitute {{{y}}} in 2
{{{x(-7)=y+42}}}........2
-----------------------------------
{{{x(-7)=(x+6)+42}}}........2.....solve for {{{x}}}

{{{-7x=x+6+42}}}
{{{-7x-x=48}}}
{{{-8x=48}}}
{{{x=48/(-8)}}}
{{{x=-6}}}

now, find {{{y}}}
{{{x+6=y}}}............1..plug in {{{x=-6}}}
{{{-6+6=y}}}

{{{0=y}}}

so, the integers are:{{{x=-6}}} and {{{y=0}}}