EXPLANATION:
Given;
We are given the following system of inequalities;
[tex]\begin{gathered} y<-\frac{1}{3}x+5---(1) \\ y>-\frac{1}{3}x-1---(2) \end{gathered}[/tex]
Required;
We are required to graph the inequalities on a graph paper and identify the solutions to the system of inequalities.
Step-by-step solution;
To graph each inequality, we will have to identify and plot points/coordinates on the inequality.
We shall take the first inequality for example;
[tex]\begin{gathered} When\text{ }x=0: \\ y=-\frac{1}{3}(0)+5 \\ \\ y=5 \end{gathered}[/tex]
Therefore we have the coordinates;
[tex](0,5)[/tex]
Also,
[tex]\begin{gathered} Whenx=3 \\ y=-\frac{1}{3}(3)+5 \\ \\ y=-1+5 \\ \\ y=4 \end{gathered}[/tex]
Also we have the coordinates,
[tex](3,4)[/tex]
We can use the same procedure for the other inequality and plot several coordinates. We can go ahead and plot several coordinates as much as the graph page/paper can accommodate.
Using a graphing tool, we have the inequalities as shown below;
As we can see from the graph above, there is no point of intersection between both inequalities. Hence, there is no solution to this system of inequalities.
ANSWER:
No Solution
