Question 697603


Six times the difference of two positive numbers {{{x}}} and {{{y}}} ( let {{{y}}} be smaller number) exceeds {{{4}}} by {{{21}}}.  

{{{6(x-y)+21=4}}}.....1


Three times their sum equals {{{8}}} times the smaller number

{{{3(x+y)=8y}}}.......2

now we have system to solve:


{{{6(x-y)+21=4}}}.....1
{{{3(x+y)=8y}}}.......2
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{{{6x-6y=4-21}}}.....1.....solve for {{{x}}}

{{{6x=6y-17}}}

{{{x=6y/6-17/6}}}

{{{x=y-2.833}}}....plug in 2

{{{3(y-2.833+y)=8y}}}.......2....solve for {{{y}}}

{{{3y-8.499+3y=8y}}}

{{{6y-8.499=8y}}}

{{{-8.499=8y-6y}}}

{{{-8.499=2y}}}

{{{-4.2495=y}}}

now find {{{x}}}

{{{x=-4.2495-2.833}}}

{{{x=-7.0825}}}

check:

{{{6(-7.0825-(-4.2495))+21=4}}}.....1

{{{6(-7.0825+4.2495)+21=4}}}

{{{6(-2.833)+21=4}}}

{{{-16.998+21=4}}}

{{{4.002=4}}}

{{{4=4}}}