Question 108337

given:

Two numbers (let them be {{{x}}} and {{{y}}}) have a {{{sum}}} of {{{22}}},
and we can write it as:

{{{x + y = 22}}}

 Their {{{difference}}} is {{{4}}}, and
we will write it as:

{{{x - y = 4}}}

now we have a system of equations with two unknown variables {{{x}}} and {{{y}}}

we need to solve this system, and we can do it this way:

 {{{x + y = 22}}}....first this equation solve for {{{x}}}, then substitute it in second equation

{{{x = 22 - y}}}

=> {{{x - y = 4}}} will be:

{{{(22 - y) - y = 4}}}

{{{22 - 2y = 4}}}.move {{{-2y}}} to the right, and {{{4}}} to the left

{{{22 - 4 = 2y}}}

{{{18 = 2y}}}...divide both sides by {{{2}}}

{{{9 = y}}}........second number

since {{{y = 9}}}, we will go back to the first equation and substitute it in order to calculate {{{x}}}


{{{x = 22 - y}}}

{{{x = 22 - 9}}}

{{{x = 13}}}.......first number

check:

the sum

{{{x + y = 22}}}

{{{13 + 9 = 22}}}

{{{22 = 22}}}

the difference

{{{x - y = 4}}} 

{{{13 - 9 = 4}}}

 {{{4 = 4}}}