In ten years time Mike will be twice as old as his son Ben. 10 years ago mike was 7 times as old as Ben. How old are Mike and Ben now?

Okay here you need to use two variables, one for Mike and one for Ben.  So X is Mike and Y is Ben.  When you use two variables you have to have at least two equations, and two is enough here.  What do we know? First equation is the first sentence.  2X= Y + 10, or in ten years Ben will reach twice Mike's age.  Now you could set up a second equation, and solve for Y but why bother? What Y would work if Ben has to be >0 to be alive? And somewhere in her Mike has to be 7 times that old.  Start with one, well that gives you Mike as 7, people at 7 don't have children.  Try two, okay that would make Mike 14 or 12 at birth, a little young, but, that works with the first equation. Hum, another way to check, and see how old they are.  When do we have Mike at twice the age of Ben, so we add in the second factor of '10 years from now'. what numbers happen if we look at the 2, well 2+10 is 12 and the double of that is 24.  So, Mike is 24, and Ben is twelve.  You can check out other ages for Ben and none of them work.  This is what you do if you have forgotten how to do the algebra properly.  As I have.