Question 918406
The number:  10T+U.
Description transcribed:  {{{T+U=7}}} and {{{10U+T-(10T+U)=9}}}.


Be sure you understand that and can work with those equations.



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The "increase by 9" equation:
{{{10U+T-10T-U=9}}}
{{{9U-9T=9}}}
{{{highlight_green(U-T=1)}}}


Simplified system is now identifiable.
{{{highlight(system(U+T=7,U-T=1))}}}
This system is perfectly ready for solving using the elimination method.


Subtract corresponding members of the equations.
{{{2T=6}}}
{{{T=3}}}
;
Add corresponding members of the equations.
{{{2U=8}}}
{{{U=4}}}
;
The original number is {{{highlight(3*10+4*1=highlight(34))}}}.