Question

Which system of linear inequalities is graphed?

Answer 1

Answer:

D. $y\geq 3x - 2\\x + 2y\leq 4$

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 $\geq \textrm{ or }\leq$.

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 $(0,2)$.

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

Option A:

$y < 3x-2\\ 2 < 3(0)-2\\2$

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

Option B:

$y < 3x - 2\\ 24\\4>4$

Both the inequalities are wrong.

Option C:

$y > 3x - 2\\2>3(0)-2\\2>-2\\\\x + 2y < 4\\0+2(2)$

Inequality 2 is wrong.

Option D:

$y\geq 3x - 2\\2\geq 3(0)-2\\2\geq -2\\\\x + 2y\leq 4\\0+2(2)\leq 4\\4\leq 4$

Here, both inequalities are correct.

So, option D is the correct answer.