7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a5a5dd8b-1438-4698-929a-c5e3d5ed0694-18_737_951_301_587}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The region \(R _ { 1 }\), shown shaded in Figure 2, is defined by the inequalities
$$0 \leqslant y \leqslant 2 \quad y \leqslant 10 - 2 x \quad y \leqslant k x$$
where \(k\) is a constant.
The line \(x = a\), where \(a\) is a constant, passes through the intersection of the lines \(y = 2\) and \(y = k x\)
Given that the area of \(R _ { 1 }\) is \(\frac { 27 } { 4 }\) square units,
- find
- the value of \(a\)
- the value of \(k\)
- Define the region \(R _ { 2 }\), also shown shaded in Figure 2, using inequalities.