Question 1210241



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


if two numbers multiply to {{{-16}}}, we have

{{{x*y=-16}}}..........solve for {{{x}}}

{{{x=-16/y}}}............eq.1



if two numbers  add to {{{15}}}, we have

{{{x+y=15}}}.........eq.2..............substitute {{{x }}}from eq.1

{{{-16/y+y=15}}}.........multiply by{{{ y}}}

{{{-16+y^2=15y}}}

{{{y^2-15y-16=0}}}......factor

{{{y^2+y-16y-16=0}}}

{{{(y^2+y)-(16y+16)=0}}}

{{{y(y+1)-16(y+1)=0}}}

{{{(y - 16) (y + 1) = 0}}}


solutions:

{{{y=16}}} or {{{y=-1}}}


then

{{{x=-16/y=-16/16=-1}}} 

or

{{{x=-16/-1=16}}}



answer:
{{{x=-1}}}
{{{y=16}}}


or
{{{x=16}}}
{{{y=-1}}}