Question

Which system of linear inequalities is represented by the graph?

Answer 1

Answer:

The system of linear inequalities is represented by the graph is:

          $y>\dfrac{2}{3}x+3\ ,\ y\leq -\dfrac{1}{3}x+2$

Step-by-step explanation:

Clearly from the graph we could observe that as one of the inequality is a strict inequality while the other is a inequality with a equality sign.

Since, one of line is dotted and the other is a solid line.

Also, we see that:

• The dotted line is a line passing through (-3,1) and (0,3)

Hence, the equation of line is:

$y-1=\dfrac{3-1}{0-(-3)}\times (x-(-3))\\\\\\y-1=\dfrac{2}{3}\times (x+3)\\\\\\y=\dfrac{2}{3}x+2+1\\\\\\y=\dfrac{2}{3}x+3$

and also we could see that the shaded region is away from the origin.

                   Hence, the inequality is:

                                  $y>\dfrac{2}{3}x+3$

• Similarly the other equation is a solid line passing through (6,0) and (0,2)

Hence, the equation of this line is:

$y-0=\dfrac{2-0}{0-6}\times (x-6)\\\\\\y=\dfrac{2}{-6}\times (x-6)\\\\\\y=-\dfrac{1}{3}x+2$

Also, the shaded region is towards the origin.

                      Hence, the inequality that holds true is:

                              $y\leq -\dfrac{1}{3}x+2$

Answer 2

The answer for this is B.