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 [tex]y+4=x[/tex]. The second fact gives you the equation [tex]3x+4y=47[/tex]. This is now a systems of equations. In order to make it a single-variable equation, multiple the [tex]y+4=x[/tex] by 3, so it will now look like [tex]3y+12=3x[/tex] and move around the variables to match the second equation. It will ultimately look like [tex]3x-3y=12[/tex]. Now subtract both equations from each other and you should be left with [tex]7y=35[/tex]. Divide both sides by 5 and you now know that [tex]y=5[/tex]. Plug the y-value that found back into the equation and solve. If [tex]y=5[/tex], then [tex]x=9[/tex]. So the number was 95.
