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If this is my solution set : x1=-x3, x2=-x3, and x3 is a free variable. Then in this case am i allowed to take any value for x3. Like lets say 1,2,3,.. ?
Correct. A typical way of expressing that freedom is :\[x_{1}=-t\]\[x_{2}=-t\]\[x_{3}=t\]\[t\in R\]in geometric terms that's a line in the direction of the vector :\[\left[\begin{matrix}1 \\ 1\\-1\end{matrix}\right]\]or written as :\[t\left[\begin{matrix}1 \\ 1\\-1\end{matrix}\right]\]so you select a point on the line by choosing a value for t