Question 1061260
The digits question


{{{10t+u}}}, the two-digit number.


{{{system(abs(t-u)=2,10u+t=-18+(10t+u))}}}



{{{10u+t=10t+u-18}}}
{{{9u=9t-18}}}
{{{u=t-2}}}
Try substituting this into the absolute value equation.


{{{abs(t-(t-2))=2}}}
{{{abs(t-t+2)=2}}}
{{{abs(2)=2}}}------------always true.


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START AGAIN TO SOLVE:
Assume {{{t>u}}}, for t TENS and u ONES.
{{{system(t-u=2, 10u+t=10t+u-18)}}},  knowing that when digits switched, new number is smaller;


{{{9u=9t-18}}}
{{{u=t-2}}}
{{{t-2=u}}}
{{{t-u-2=0}}}
{{{highlight(t-u=2)}}}


The description is essentially ONE equation in TWO unknown variables.
Solution set:
31, 42, 53, 64, 75, 86, 97, 20