Question 1192151
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A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. 
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{{{x=(1/2)y-3}}}, the meaning of the first sentence.
{{{x+3=y/2}}}
{{{y=2x+6}}}


Your second sentence, {{{y=10(x-1)}}}.


Each of the two is a completely different equation.  They are not equivalent.  Completely separate situations!