Question

if 10-x = y , then does 20-2x always equal 2y?

Answer 1

Yes it is. You have multiplied the equation by 2. You can confirm this by drawing a graph of x against y.

Answer 2

if you can divide 20-2x=2y to get 10-x=y, then it confirms that it will always be 2y.
The same would apply to 30-3x=3y