(x+2)(x+1)=(x-2)(x-3) (y+3)(y+2)=(y-1)(y-2)
Answers
I will be guilty about this one. The real mathematical solution is really going through the arithmetic, and you will get results in a fairly long process. And I am sure you will get answers showing you that. But I am a lazy person and always loved to simplify things. As a teacher I always encouraged my students to do more thinking than mechanically follow procedures. So: let us look at the problems that needs to be solved critically. Can we think of a number squared and an other plain number adding up to 11? Well we can think of x being 1, but then y must be 10. That won’t satisfy the second equation. Similarly X may be 2, but then y must be 7, and that won’t satisfy the second equation either. OK. Let us try X=3. then to satisfy the first equation Y must be 2. 9+2=11
How about the second equation? 4+3=7 Right!
We have the answer. x=3 and y=2.
If you prefer the long mechanical way: be my guest!