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Which of the following describes the set of solutions for the system of equations:$$\left\{\begin{array}{rcrcrcr} x &+& y &+& z &=& 3 \\ x &-& y &+& 2z &=& 2\end{array}\right.$$
\(x=1, y=1, z=1\)
\(x = \frac{5}{2} + \frac{3}{2}t, \quad y = \frac{1}{2} - \frac{1}{2}t, \quad z = t\), for all \(t\in\R\)
\(x=t, y=1-t, z=2\), for all \(t\in\R\)
\(x = \frac{5}{2} - \frac{3}{2}t, \quad y = \frac{1}{2} + \frac{1}{2}t, \quad z = t\), for all \(t\in\R\)
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