Show that the system of equations
$$\begin{aligned}
& x - y + 2 z = 4 \\
& x - y - 3 z = a \\
& x - y + 7 z = 13
\end{aligned}$$
where \(a\) is a constant, does not have a unique solution.
Given that \(a = - 5\), show that the system of equations in part (a) is consistent. Interpret this situation geometrically.
Given instead that \(a \neq - 5\), show that the system of equations in part (a) is inconsistent. Interpret this situation geometrically.
2 (a) Show that the system of equations
$$\begin{aligned}
& x - y + 2 z = 4 \\
& x - y - 3 z = a \\
& x - y + 7 z = 13
\end{aligned}$$
where $a$ is a constant, does not have a unique solution.\\
(b) Given that $a = - 5$, show that the system of equations in part (a) is consistent. Interpret this situation geometrically.\\
(c) Given instead that $a \neq - 5$, show that the system of equations in part (a) is inconsistent. Interpret this situation geometrically.\\
\hfill \mbox{\textit{CAIE Further Paper 2 2022 Q2}}