Itemb.iv

If \(y=0\text{,}\) then we arrive at the system of three linear equations:

\begin{equation*} \begin{alignedat}{4} x \amp \amp \amp {}={} \amp 3 \\ \amp {}-{} \amp z \amp {}={} \amp 2 \\ 2x \amp {}+{} \amp z \amp {}={} \amp 4. \\ \end{alignedat} \end{equation*}

We have a solution when \(x=3\) and \(z=-2\text{.}\) Therefore, \((x,y,z)=(3,0,-2)\) is a solution to the original system of equations.

in-context