The graphical solution set of the system of inequations \(x+y \geq 1,7 x+9 y \leq 63, y \leq 5, x \leq 6\), \(x \geq 0, y \geq 0\) is represented by

Fig. 2

(i) \(x+y \geq 1,7 x+9 y \leq 63, x \leq 6, y \leq 5, x \geq 0, y \geq 0\)
First, we shall plot the graph of the equation and shade the side containing solutions of the inequality,
Now, we can choose any value but find the two mandatory values which are at \(x=0\) and \(y=0\), i.e., \(x\) and \(y\)-intercepts always,
\(x+y \geq 1\)
Therefore when,
\(\begin{array}{|c|c|c|c|}\hline x & 0 & 2 & 1 \\ \hline y & 1 & -1 & 0 \\ \hline\end{array}\)
\(7 x+9 y \leq 63\)
Therefore when,
\(\begin{array}{|l|l|l|l|}\hline x & 0 & 5 & 9 \\ \hline y & 7 & 3.11 & 0 \\ \hline\end{array}\)
\(x \leq 6, y \leq 5 \text { and } x \geq 0, y \geq 0\)