Question

This graph represents 2x+y=−4.

Which ordered pair is in the solution set of 2x+y≤−4?

(A) (−2, 2)

(B) (2, −2)

(C) (−2, −2)

(D) (2, 2)

Answer 1

C) (−2, −2)

Explanation:

Inequalities

We are given the inequality:

2x + y ≤ -4

Any orderer pair that belongs to the solution of the above inequality must make it true.

Let's test each of the following options:

(A) (-2,2) For x=-2 and y=2:

2(-2) + 2 ≤ -4

-4 + 2 ≤ -4

-2 ≤ -4

The inequality is false, thus this option is not correct

(B) (2,-2) For x=2 and y=-2:

2(2) - 2 ≤ -4

4 - 2 ≤ -4

2 ≤ -4

The inequality is false, thus this option is not correct

(C) (-2,-2) For x=-2 and y=-2:

2(-2) - 2 ≤ -4

-4 - 2 ≤ -4

-6 ≤ -4

The inequality is true, thus this option is correct.

(D) (2,2) For x=2 and y=2:

2(2) + 2 ≤ -4

4 + 2 ≤ -4

6 ≤ -4

The inequality is false, thus this option is not correct

Answer: (C) (−2, −2)