Answer:
[tex]\begin{gathered} 2x-y\leq8 \\ x+y\leq5 \\ x\ge0 \\ y\ge0 \end{gathered}[/tex]Step-by-step explanation:
To determine the inequalities that represent the graph, we need to find the equations for the lines on the graph.
The line is represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore, if the line goes down, has a y-intercept of 5, we can calculate the slope with change in y over change in x:
[tex]\begin{gathered} m=\frac{0-5}{5-0} \\ m=-1 \end{gathered}[/tex]The equation of the line is:
[tex]\begin{gathered} y=-x+5 \\ \text{ Since the shaded region is below the line:} \\ x+y\leq5 \end{gathered}[/tex]The shaded region also has limits with x=0 and y=0, then:
[tex]\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}[/tex]For the other line, which has a y-intercept of -8 and rate of change (slope):
[tex]\begin{gathered} m=\frac{6-0}{7-4} \\ m=2 \end{gathered}[/tex]Its equation would be:
[tex]\begin{gathered} y=2x-8 \\ \text{ Since the shaded region is on the left:} \\ 2x-y\leq8 \end{gathered}[/tex]