Solve the following system of inequalities graphically: $x+y \leq 9, y>x, x \geq 0$.

(N/A) $x+y \leq 9$ .... $(1)$
$y>x$ .... $(2)$
$x \geq 0$ .... $(3)$
The graph of the lines,$x+y=9$ and $y=x$,are drawn in the figure below.
Inequality $(1)$ represents the region below the line $x+y=9$ (including the line $x+y=9$). It is observed that $(0,1)$ satisfies the inequality $y>x$ $[1>0]$. Therefore,inequality $(2)$ represents the half-plane corresponding to the line $y=x$,containing the point $(0,1)$ (excluding the line $y=x$). Inequality $(3)$ represents the region on the right-hand side of the line $x=0$ or $y$-axis (including the $y$-axis).
Hence,the solution of the given system of linear inequalities is represented by the common shaded region including the points on the lines $x+y=9$ and $x=0$,and excluding the points on the line $y=x$ as shown in the figure.