The ones digit of a two digit number is four less than the tens digit. the sum of three times the tens digit and four times the ones digit is 47. find the number and show your work

Say that the two digit number you have is xy, which is really 10x+y (making it a two-digit number). Based from the first fact, you have the equation . The second fact gives you the equation . This is now a systems of equations. In order to make it a single-variable equation, multiple the by 3, so it will now look like and move around the variables to match the second equation. It will ultimately look like . Now subtract both equations from each other and you should be left with . Divide both sides by 5 and you now know that . Plug the y-value that found back into the equation and solve. If , then . So the number was 95.