Question

Which ordered pairs are solutions to the inequality 2x+y>−4?

Select each correct answer.
A). (5, −12)
B). (−3, 0)
C). (−1, −1)
D). (0, 1)
E). (4, −12)

Answer 1

A , C , D

Step-by-step explanation:

To determine which ordered pairs are solutions to the inequality.

substitute the coordinates for x and y into the left side and compare result with right side

A (5, - 12 )

2(5) + (- 12) = 10 - 12 = - 2 > - 4 ← solution

B (- 3, 0 )

2(- 3) + 0 = - 6 + 0 = - 6 < - 4 ← not a solution

C (- 1, - 1 )

2(- 1) + (- 1) = - 2 - 1 = - 3 > - 4 ← solution

D (0, 1 )

2(0) + 1 = 0 + 1 = 1 > - 4 ← solution

E (4, - 12 )

2(4) + (- 12) = 8 - 12 = - 4 , not > - 4 ← not a solution

Answer 2

After testing each ordered pair in the inequality 2x + y > -4, only the ordered pair (0, 1) satisfies the inequality.

Step-by-step explanation:

To determine which ordered pairs are solutions to the inequality 2x + y > -4, we substitute the x and y values from each ordered pair into the inequality to see if it holds true.

• For (5, −12), substitute x=5 and y=−12 into the inequality: 2(5) + (−12) = 10 − 12 = −2, which is not greater than −4.
• For (−3, 0), substitute x=−3 and y=0 into the inequality: 2(−3) + 0 = −6, which is not greater than −4.
• For (−1, −1), substitute x=−1 and y=−1 into the inequality: 2(−1) + (−1) = −2 − 1 = −3, which is not greater than −4.
• For (0, 1), substitute x=0 and y=1 into the inequality: 2(0) + 1 = 1, which is greater than −4.
• For (4, −12), substitute x=4 and y=−12 into the inequality: 2(4) + (−12) = 8 − 12 = −4, which is equal to −4 and does not satisfy the inequality.

The only ordered pair that makes the inequality true is (0, 1).