Question

Hello, how do I state coordinates for linear inequality systems?

Answer 1

(8,2)

Step-by-step explanation:

Given the system of inequalities:

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

First, we determine the x and y-intercepts of each inequality to plot the boundary line.

`\begin{gathered} y=(1)/(3)x-5 \\ \text{When x=0,y=-5}\implies(0,-5) \\ \text{When y=0} \\ (1)/(3)x=5 \\ x=15\implies(15,0) \end{gathered}`

Since we have the greater than sign, shade above the boundary line.

For the second inequality:

`\begin{gathered} y>-x+3 \\ \text{Boundary Line:}y=-x+3 \\ \text{When x=0,y=3}\implies(0,3) \\ \text{When y=0,x=3}\implies(3,0) \end{gathered}`

Since we have the greater than sign, shade above the boundary line.

Any point in the region where the two graphs intersect (shaded purple) is a solution to the system of inequalities.

• One point is (8,2).

You can pick as many points as possible.