Question 915066
The number originally could be T*10+U, using U for the ones digit and T for the tens digit.


Translate the description.
{{{U=1+2T}}}


Next part of the description needs care.
For {{{U*10+T}}}, condition is that {{{cross((U*10+T)=-3+(T*10+U))}}}. (Go to NEW INFORMATION, below here.)


You have two linear equations in the unknown variables, U and T.
Simplify the second part of the description, and then you could substitute for U from the first part of the description.



A FEW STEPS  ---(NO.  Go to NEW INFORMATION...)
{{{10U+T=10T+U-3}}}
{{{10U-U+T-10T=-3}}}
{{{9U-9T=-3}}}
{{{9T-9U=3}}}
{{{3T-3U=1}}}
you should be able to finish solving U and T.



NEW INFORMATION:
<i>"...the new number is 8 less than 3 times the original number."</i>


Changes to second equation make it then, {{{(U*10+T)=-8+3(T*10+U)}}}.
Either way, I had misunderstood part of the description.


The steps to start for simplifying this equation are straightforward:
{{{10U+T=-8+3*10*T+3U}}}
{{{10U+T=30T+3U-8}}}
{{{7U-29T=-8}}}
{{{29T-7U=8}}}
-
and your other equation from first part of the description, {{{U=1+2T}}}.


{{{highlight(system(U=1+2T,29T-7U=8))}}}
This system should be uncomplicated to solve.