Product Production System

A company manufactures two products, A and B. The production can be described by the following system of linear equations:

$$2x + 3y = 48$$

$$4x - 2y = 10$$

Here, $x$ represents the number of Product A produced, and $y$ represents the number of Product B produced. Determine the values of $x$ and $y$ that satisfy both equations simultaneously. Then calculate the value of $x - y$.