Need help with math 9 algebra/system word problem.

Question

The sum of the digits of a two-digit number is one more than three times the units digit. When the digits of the two-digit number are reversed, the number is reduced by 36. First write two equations representing the information, then solve the system to find the two-digit number.

Answer 1

Let x = units digit

      y = tens digit

 

A two digit positive integer can be expressed as

10y + x where y is the tens digit and x is the units digit.  For example, 37 = (10)(3) + 7.

 

So, we have the following system of equations:

 

x + y = 3x + 1

10x + y = (10y + x) - 36

 

-2x + y = 1

9x - 9y = -36

 

Since -2x + y = 1, y = 2x + 1

 

Replace y by 2x + 1 in the equation 9x - 9y = -36:

 

9x - 9(2x + 1) = -36

        -9x -9 = -36

              -9x = -27

                 x = 3 and y = 2x + 1 = 7

 

The number is 73