Answer to Question #153595 in Algebra for Rajanikanth R

Question

The sum of the digits of a two-digit number is 8. The result of subtracting the units digit from the tens digit is -4. Define the variables and write the system of equations that can be used to find the number. Then solve the system and find the number.

Answer 1

Solution. Represented two-digit number as xy. According to the condition of the problem

$$x+y=8$$

also

$$x-y=-4$$

As a result, we obtain the system of equations

We solve the system of equations. Let us add the first and second equations of the system

$$x+y+x-y=8-4$$

Hence, get

$$2x=4$$

$$x=2$$

Substituting the obtained value of x into the first equation, we obtain

$$2+y=8$$ $$y=6$$

As a result, the number is

$$26$$

Answer: 26.