Question 111467
You need to first express the problem symbolically.  First thing you need are symbols for the two numbers, so let's call them {{{n[1]}}} and {{{n[2]}}}.
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The first fact we know is that the difference of these two numbers is 7.  So, let's call {{{n[2]}}} the larger of the two numbers, so we can write {{{n[2]-n[1]=7}}}
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Our next fact says "The second is 7 less than 2 times the first."  So let's write:
{{{n[2]=2n[1]-7}}}
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Since the second equation gives us an expression for {{{n[2]}}} directly, let's just substitute into the first equation:
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{{{2n[1]-7-n[1]=7}}}
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Add 7 to both sides and collect terms to get:
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{{{n[1]=14}}}
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Now put this value back into equation 1:
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{{{n[2]-14=7}}}, so
{{{n[2]=21}}}
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Last step, check your answer.
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{{{21-14=7}}}, and
{{{21=2(14)-7}}}.  Since both of those statements are true, the answer checks.