Question 268900
"The sum of two numbers is fourteen." {{{A+B=14}}} 
"difference between two times the smaller and the larger is one" so {{{A>B}}} where {{{2B-A=1}}}
now you have 2 equations use substitution method and solve.
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{{{A+B=14}}}
{{{2B-A=1}}}
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{{{A+B=14}}}
{{{B=14-A}}}
{{{2(14-A)-A=1}}}
{{{28-2A-A=1}}}
{{{28-3A-28=1-28}}}
{{{-3A/-3=-27/-3}}}
{{{A=9}}}
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{{{2B-9=1}}}
{{{2B=10}}}
{{{B=5}}}
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CHECK
{{{A+B=14}}}
{{{9+5=14}}}
{{{14=14}}}
CORRECT