Question 1158446
{{{x+y=115}}}..........eq.1 
{{{x+y=21}}}...........eq.2 

Translate to a system of equations and solve:

The sum of two numbers is {{{115}}}. ->correct
The difference is {{{21}}}.  ->incorrect=>{{{x+y=21}}} is also the sum of two numbers 

{{{x+y=115}}}..........eq.1 
{{{x+y=21}}}...........eq.2
----------------------------subtract eq.2 from eq.1

{{{x+y-(x+y)=115-21}}}

{{{x+y-x-y=94}}}

{{{0=94}}}-> no solution exist (equations above represent two parallel lines)

{{{ graph( 600, 600, -10, 125, -10, 125, 115-x,21-x) }}} 



but, if you made mistake typing {{{x+y=21}}} and if it is acctualy difference, then you have

{{{x-y=21}}}...........eq.2

and system is


{{{x+y=115}}}..........eq.1 
{{{x-y=21}}}...........eq.2
----------------------------subtract eq.2 from eq.1

{{{x+y-(x-y)=115-21}}}

{{{x+y-x+y=94}}}

{{{2y=94}}}

{{{y=47}}}

go to

{{{x-y=21}}}...........eq.2, plug in {{{y}}} value

{{{x-47=21}}}

{{{x=21+47}}}

{{{x=68}}}


{{{drawing( 600, 600, -10, 125, -10, 125,
circle(47,68,.5),locate(47,68,p(47,68)),
 graph( 600, 600, -10, 125, -10, 125, 115-x,21+x)) }}} 


check solution:


{{{x+y=115}}}=>{{{68+47=115}}}=>{{{115=115}}} 
{{{x-y=21}}}{{{68-47=21}}}=>{{{21=21}}}