Algebraic maths word problem… HELP!!

Question

When the two digits of a two digit number are added together, the answer is 12. The two digit number obtained by swapping the digits around is 18 more than the origional number. Fine the two digits

Answer 1

Let the two digit number be xy,  The sum of the two digits is 12:

 

x + y = 12

 

The value of the number obtained by switching the digits (yx) is 18 more than the original number (xy).  Recall that the first digit is in the "tens" place and the second is in the "ones" place, so:

 

10y + x = 10x + y + 18

9y - 9x = 18

 

Solve the system of equations:

 

   x +  y  = 12

-9x + 9y = 18