Answer
\[\left\{ \begin{align}
& y>x-3 \\
& y\le x \\
\end{align} \right.\]
Work Step by Step
\[y=x-3\]It intersects x-axis at \[\left( 3,0 \right)\] and y-axis at \[\left( 0,-3 \right)\]
The slope of the line is,
\[\begin{align}
& m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\
& =\frac{-3-0}{0-3} \\
& =1
\end{align}\]
So, the equation of the line is \[y=x-3\]
The line is dashed line, the line is not included. Using the test point\[\left( 0,0 \right)\], the statement is true. The equation is \[y>x-3\]
\[y\le x\]It passes through origin, y-intercept is 0. Origin cannot be the test point. From the graph, take two ordered pairs, \[\left( 1,1 \right)\] and \[\left( 2,2 \right)\]
\[\begin{align}
& m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\
& =\frac{2-1}{2-1} \\
& =1
\end{align}\]
The line is a solid line. The equation is \[y\le x\]
The system of linear inequalities for the graph is,
\[\left\{ \begin{align}
& y>x-3 \\
& y\le x \\
\end{align} \right.\]
