Which system of inequalities represents the graph?

 The correct option is

Step-by-step explanation:  We are given to select the correct set of inequalities that represents the graph shown.

From the shaded region, let us consider a point (-6, -2).

The set of inequalities that will be satisfied by the point (x, y) = (-6, -2) is the required answer.

(1) The given set of inequalities are

For (x, y) = (-6, -2), we have

which is not possible.

So, option (1) is NOT correct.

(2) The given set of inequalities are

For (x, y) = (-6, -2), we have

true,

true,

true.

Since all the three inequalities are satisfied by the point (-6, -2), so option (2) is CORRECT.

(3) The given set of inequalities are

For (x, y) = (-6, -2), we have

true,

which is not possible.

So, option (3) is NOT correct.

(4) The given set of inequalities are

For (x, y) = (-6, -2), we have

which is not possible.

So, option (4) is NOT correct.

Thus, option (2) is CORRECT.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

m∠5 + m∠3 = m∠1   is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6   is true

m∠2 +m∠3 +m∠5 = 180   is true