Question 267268
Let t = tens digit and u = units digit



Any two digit number is of the form {{{10t+u}}} where 't' and 'u' are whole numbers. For example, the number 23 has a tens digit of 2 and a units digit of 3. So t=2 and u=3 which means that {{{10t+u=10(2)+3=20+3=23}}}



Because "The sum of the digits of a certain two-digit number is 7", we know that {{{t+u=7}}}. So this the first equation.



And since "Reversing its digits increases the number by 9", this tells us that {{{10u+t=10t+u+9}}}. This is the second equation.



I'll let you solve the system of equations.