Question

Which graph shows the solution to the system of linear inequalities?

Answer 1

Answer:

Observe the attached image.

Step-by-step explanation:

We have the following linear inequalities

$y > \frac{2}{3}x + 3\\\\y \leq \frac{1}{3}x + 2$

Graph the lines corresponding to each inequality

$y > \frac{2}{3}x + 3$ →  $y = \frac{2}{3}x + 3$

Cut with the y axis:

y = 3

Cut with the x axis:

$0 = \frac{2}{3}x + 3$

$-3 = \frac{2}{3}x$

$x = -4.5$

$y \leq \frac{1}{3}x + 2$ →  $y = \frac{1}{3}x +2$

Cut with the y axis:

y = 2

Cut with the x axis:

$0 = \frac{1}{3}x + 2$

$-2 = \frac{1}{3}x$

$x = -6$

Now graph the two lines

For $y > \frac{2}{3}x + 3$

The region is made up of all the points that are above the line $y =\frac{2}{3}x + 3$

For $y \leq \frac{1}{3}x + 2$

The region is made up of all the points that are on the line and below $y = \frac{1}{3}x +2$

The final region will be the interception of both regions

Observe the attached image.

The system shown in the image you attached is:

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