The correct answer is: A. A unique solution of x = 1, y = 1 and z = 1.
To solve this system of equations, we can use the elimination method. First, we can eliminate $z$ by adding the first and third equations together. This gives us the equation $3x + 3y = 5$. Next, we can eliminate $y$ by subtracting the second equation from the third equation. This gives us the equation $x – 2x = -4$. Solving for $x$, we get $x = 2$. Substituting $x = 2$ into the first equation, we get $2 + 2y + z = 4$. Solving for $y$, we get $y = 1$. Substituting $x = 2$ and $y = 1$ into the second equation, we get $4 + 2 + 2z = 5$. Solving for $z$, we get $z = 1$. Therefore, the unique solution of the system of equations is $x = 2$, $y = 1$, and $z = 1$.
Option B is incorrect because there are only two solutions, not three. Option C is incorrect because there is only one solution, not an infinite number of solutions. Option D is incorrect because there is a feasible solution, namely $x = 2$, $y = 1$, and $z = 1$.