Question 983813
{{{10t+u}}} is the two-digit number.


{{{system(t-u=4,4*t*u-(10t+u)=11)}}}
The first and the second sentences.


{{{system(t=u+4,4tu-10t-u=11)}}}


Substitute for t in the second equation.
{{{4(u+4)u-10(u+4)-u=11}}}
{{{4u^2+16u-10u-40-u-11=0}}}
{{{4u^2+5u-51=0}}}-----------use formula for general solution to quadratic equation.


{{{u=(-5+- sqrt(25+4*4*51))/8}}}
{{{u=(-5+- sqrt(841))/8}}}
{{{u=(-5+29)/8}}} because the MINUS form makes no sense for digits.
{{{u=24/8}}}
{{{highlight(u=3)}}}


The TENS digit:
{{{t=u+4}}}
{{{t=3+4}}}
{{{highlight(t=7)}}}