Question

On a piece of paper, graph this system of inequalities. Then determine whichanswer choice matches the graph you drew and identify the number ofsolutions.y-x-11X-

Answer 1

Step-by-step explanation:

Given;

We are given the following system of inequalities;

`\begin{gathered} y<-(1)/(3)x+5---(1) \\ y>-(1)/(3)x-1---(2) \end{gathered}`

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;

`\begin{gathered} When\text{ }x=0: \\ y=-(1)/(3)(0)+5 \\ \\ y=5 \end{gathered}`

Therefore we have the coordinates;

`(0,5)`

Also,

`\begin{gathered} Whenx=3 \\ y=-(1)/(3)(3)+5 \\ \\ y=-1+5 \\ \\ y=4 \end{gathered}`

Also we have the coordinates,

`(3,4)`

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