The correct answer is $\boxed{\text{B}}$.
To solve a system of equations, we can use the elimination method. In this method, we eliminate one variable at a time by adding or subtracting the equations in a specific way.
For the given system of equations, we can eliminate $x$ by adding the first and third equations together. This gives us the equation $7y + 7z = 3$. We can then eliminate $y$ by adding the second and third equations together. This gives us the equation $7z = 4$. Solving for $z$, we get $z = \frac{4}{7}$.
We can then substitute $z = \frac{4}{7}$ into the first equation to solve for $x$. This gives us the equation $x + 2y + 4 \left( \frac{4}{7} \right) = 2$. Solving for $x$, we get $x = -\frac{2}{7}$.
We can then substitute $z = \frac{4}{7}$ and $x = -\frac{2}{7}$ into the second equation to solve for $y$. This gives us the equation $4 \left( -\frac{2}{7} \right) + 3y + \frac{4}{7} = 5$. Solving for $y$, we get $y = \frac{1}{7}$.
Therefore, the system of equations has two solutions: $\boxed{x = -\frac{2}{7}, y = \frac{1}{7}, z = \frac{4}{7}}$.
Here is a brief explanation of each option:
- Option A: Unique solution. This means that there is only one solution to the system of equations.
- Option B: Two solutions. This means that there are two solutions to the system of equations.
- Option C: No solutions. This means that there is no solution to the system of equations.
- Option D: More than two solutions. This means that there are more than two solutions to the system of equations.