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Suppose that you are given the collection $S=\{(s,-s,t): s, t \text{ free} \}$ of vectors in $R^3$.

Which of the following systems has $S$ as its solution set?

$\begin{align*} x + y &= 0 \\\ 0z & = 0 \end{align*}$

$\begin{align*} x + y &= 0 \\\ z& = 0 \end{align*}$

$\begin{align*} x - y & = 0 \\\ 0z & = 0 \end{align*}$

$\begin{align*} x - y & = 1 \\\ 0z & = 1 \end{align*}$

None of the above have $S$ as solution set.