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NEED ASAP plz. I will also mark brainiest! Don't just take points, I will report you.

The coordinate plane below represents a community. Points A through F is housed in the community.

Part A: Using the graph above, create a system of inequalities that only contains points A and B in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.

Part B: Explain how to verify that the points A and B are solutions to the system of inequalities created in Part A.

Part C: Billy wants to live in the area defined by y < 3x − 6. Explain how you can identify the houses in which Billy is interested in living.

NEED ASAP plz I will also mark brainiest Dont just take points I will report you The coordinate plane below represents a community Points A through F is housed class=

Respuesta :

Part A:

You may choose the two lines connecting the origin and points A and B, and choose the portion of the space between them.

The line between the origin and A is

[tex]y = 3x[/tex]

We want everything below this line (line included), so the first inequality is

[tex]y \leq 3x[/tex]

The line between the origin and B is

[tex]y = \dfrac{1}{3}x[/tex]

We want everything above this line (line included), so the second inequality is

[tex]y \geq \dfrac{1}{3}x[/tex]

Create a system with these two inequalities and you'll have an area including only points A and B

Part B:

To verify the solutions, we can plug the coordinates of A and B in this system and check that we get something true: the coordinates of point A are (1,3), while the coordinates of point B are (3,1). The system becomes:

[tex]A:\begin{cases}3 \leq 3\cdot 1\\3 \geq \frac{1}{3}\cdot 1\end{cases},\quad B:\begin{cases}1 \leq 3\cdot 3\\1 \geq \frac{1}{3}\cdot 3\end{cases}[/tex]

Which means

[tex]A:\begin{cases}3 \leq 3\\3 \geq \frac{1}{3}\end{cases},\quad B:\begin{cases}1 \leq 9\\1 \geq 1\end{cases}[/tex]

And these are all true. So, the system is satisfied, which means that the points belong to the shaded area.

Part C

If you draw the line, you'll see that the only points that lay below the line are B and C. In fact, if we plug the coordinates we have

[tex]B:\ 1 <3\cdot 3 - 6 \iff 1 < 3,\quad C:\ -3 < 3\cdot 3 - 6 \iff -3 < 3[/tex]

And this are both true. You can check the coordinates of all other points, and see that they won't satisfy the inequality y<3x-6