Let the system of linear equations
$$x + y + kz = 2$$
$$2x + 3y - z = 1$$
$$3x + 4y + 2z = k$$
have infinitely many solutions. Then the system
$$(k+1)x + (2k-1)y = 7$$
$$(2k+1)x + (k+5)y = 10$$ has:

A

infinitely many solutions

B

unique solution satisfying $$x - y = 1$$

C

no solution

D

unique solution satisfying $$x + y = 1$$