B2. Let $x$ and $y$ be integers. If the first number is divided by the second number, the quotient is 2 and the remainder is 2. If the sum of the numbers $x$ and $y$ is divided by their difference, the quotient is 2 and the remainder is 8. Determine $D(x, y)$ and $v(x, y)$.
B2. Considering the fundamental theorem of division of integers, we set up the equations $x=2 y+2$ and $x+y=2(x-y)+8$. We organize and solve the system. The solution to the system is $x=22$ and $y=10$. These are the sought numbers. We determine $D(22,10)=2$ and $v(22,10)=110$.
Writing the first equation $x=2 y+2$ ..... 1 point
Writing the second equation $x+y=2(x-y)+8$ ..... 1 point
Organizing the system... ..... 1 point
Solving the system of equations ..... $1^{*}$ point
Solution to the system of equations $x=22, y=10$ ..... 2 points
Determination of $D(22,10)=2, v(22,10)=110$ ..... 2 points