Determine whether the expression is invariant of the assignment?

Question

Assignment x,y :=x+1, y-1
Expression 2*y-x

Answer 1

substitute the assignment in the expression and see if you get the same:

2(y-1) -(x+1)
2y-2-x-1
2y -x -3,
therefore it is not invariant

Answer 2

2y-x -> 2(y-1)-(x+1) = 2y-2-x-1 = 2y-x-3, so no, it's not invariant.

Just for fun: let x,y := x+a, y+b.

2y-x -> 2(y+b)-(x+a) = 2y+2b-x-a=(2y-x)+2b-a. So, if a=2b, then it is invariant.