\(\mathbb{S_1}:\)
\(\begin{eqnarray*} x + y &=& 1\\ 2x + y &=& -1 \end{eqnarray*}\)
Solving the first equation for \(y\) in terms of \(x\) yields \(y = 1 - x\).
Substituting \(y = 1 - x\) into the second equation and simplifying yields \(x +1 = -1\). So \(x = -2\).
Since \(y = 1 - x\), then \(y = 3\).