Respuesta :

The system of linear inequalities are given by the in the question, that

describes the inequalities.

The system of linear inequalities represented by the graph is the option;

  • y ≥  (1/3)·x + 3 and 3·x - y > 2

Reasons:

The points on the given graph are;

(3, 4), and (-3, 2)

The slope is; (2 - 4)÷((-3) - 3) = 1/3

The equation is;

y - 4 = (1/3)·(x - 3)

y = (1/3)·x - 1 + 4 = (1/3)·x + 3

Therefore;

  • The graph is y ≥  (1/3)·x + 3

Point on the second graph are;

(0, -2) and (2, 4)

The slope is; (4 - (-2)) ÷ (2 - 0) = 3

The equation is; y - (-2) = 3·(x - 0)

y = 3·x - 2

  • The inequality is; y < 3·x -2

Which gives;

2 < 3·x - y

Therefore;

3·x - y > 2

The correct option is the first option;

  • y ≥  (1/3)·x + 3 and 3·x - y > 2

Learn more about linear inequalities here:

https://brainly.com/question/371134

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