Which system of linear inequalities is graphed?

a. y < 3x-2
x + 2y ≥ 4

b. y < 3x - 2
x + 2y > 4

c. y > 3x - 2
x + 2y < 4

d. y ≥ 3x - 2
x + 2y ≤ 4

D.

Step-by-step explanation:

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either .

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line. Let us take .

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Option A:

So, inequality 1 is wrong as -2 is less than 2.

Option B:

Both the inequalities are wrong.

Option C:

Inequality 2 is wrong.

Option D:

Here, both inequalities are correct.

So, option D is the correct answer.

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step-by-step explanation: