Question 392228
the greater of two numbers is 1 more than twice the smaller. three times the greater exceeds five times the smaller by 10. find the numbers


let numbers be {{{x}}} and {{{y}}}, and let {{{x<y}}} 

given:

he greater of two numbers is {{{1}}}more than twice the smaller; so,we will have


{{{y = 2x + 1}}}........................(1)


three times the greater exceeds five times the smaller by {{{10}}}


{{{3y = 5x + 10}}}........................(2)


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solve a system


{{{y = 2x + 1}}}........................(1)

{{{3y = 5x + 10}}}........................(2)

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{{{y = 2x + 1}}}........................(1).......substitute {{{y}}} in.....(2)


{{{3(2x + 1) = 5x + 10}}}........................(2)...solve for {{{x}}}


{{{6x + 3 = 5x + 10}}}


{{{6x - 5x = 10 -  3}}}


{{{x = 7}}}........................now find {{{y}}}


{{{y = 2x + 1}}}........................(1).substitute {{{x}}}


{{{y = 2*7 + 1}}}


{{{y = 14+ 1}}}

{{{y = 15}}}


the numbers are: {{{x = 7}}} and {{{y = 15}}}