Itemb

Consider the system of linear equations:

\begin{equation*} \begin{alignedat}{4} x \amp {}+{} \amp y \amp \amp \amp {}={} \amp 3 \\ \amp \amp y \amp {}-{} \amp z \amp {}={} \amp 2 \\ 2x \amp {}+{} \amp y \amp {}+{} \amp z \amp {}={} \amp 4. \\ \end{alignedat} \end{equation*}
  1. Is \((x,y,z) = (1,2,0)\) a solution?

  2. Is \((x,y,z) = (-2,1,0)\) a solution?

  3. Is \((x,y,z) = (0,-3,1)\) a solution?

  4. Can you find a solution in which \(y = 0\text{?}\)

  5. Do you think there are other solutions? Please explain your response.

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