This is one of the Diophantine equations. The solution is usually positive integers. This is an exception. It either requires fractions (I hope not) or negative numbers.
So let's see what we have.
Let's start with some obvious statements.
Is there any kind of integer that will solve this? My inclination is to say no. 911 is an odd number. How can 2 evens be manipulated to give an odd? No way using integers that I know of. So it looks like there are an infinite number of real solutions but no integers.
946x+642y=911
Is there any common factor to each of the numbers? Put another way, is 911 prime? The other two are not. 911 is prime. Our next step is to graph it. Maybe that will tell us something. We get the x and y intercepts, but nothing near an answer. You can go to desmos yourself and put this graph in. Just click on any point that looks reasonable to you. They are all give at least 1 decimals.
I think your teacher is just trying to work with awkward numbers. So work with awkward numbers. You could always just put in say 3 for x and solve for y.
