Which of the following would be a solution to the inequality 3𝑥 + 2𝑦 ≥ 7?

Question

Which of the following would be a solution to the inequality 3𝑥 + 2𝑦 ≥ 7?

a) (0, 0)
b) (− 1, 5)
c) (0, − 4)
d) (2, 0)

Answer 1

To determine which of the given points is a solution to the inequality 3𝑥 + 2𝑦 ≥ 7, we substitute the x- and y-coordinates of each point into the inequality and check if it is true.

a) (0, 0):
3(0) + 2(0) = 0 + 0 = 0
Since 0 is not greater than or equal to 7, (0, 0) is not a solution.

b) (− 1, 5):
3(-1) + 2(5) = -3 + 10 = 7
Since 7 is greater than or equal to 7, (− 1, 5) is a solution.

c) (0, − 4):
3(0) + 2(-4) = 0 - 8 = -8
Since -8 is not greater than or equal to 7, (0, − 4) is not a solution.

d) (2, 0):
3(2) + 2(0) = 6 + 0 = 6
Since 6 is not greater than or equal to 7, (2, 0) is not a solution.

Therefore, the only solution to the inequality 3𝑥 + 2𝑦 ≥ 7 is (− 1, 5), option b).

Answer 2

To find the solution to the inequality 3𝑥 + 2𝑦 ≥ 7, we can substitute the given values from each option into the inequality and check if it is true or false. Let's go through each option:

a) (0, 0):
Substituting x = 0 and y = 0 into the inequality:
3(0) + 2(0) ≥ 7
0 ≥ 7
This is false, so (0, 0) is not a solution.

b) (− 1, 5):
Substituting x = -1 and y = 5 into the inequality:
3(-1) + 2(5) ≥ 7
-3 + 10 ≥ 7
7 ≥ 7
This is true, so (− 1, 5) is a solution.

c) (0, − 4):
Substituting x = 0 and y = -4 into the inequality:
3(0) + 2(-4) ≥ 7
0 - 8 ≥ 7
-8 ≥ 7
This is false, so (0, − 4) is not a solution.

d) (2, 0):
Substituting x = 2 and y = 0 into the inequality:
3(2) + 2(0) ≥ 7
6 + 0 ≥ 7
6 ≥ 7
This is false, so (2, 0) is not a solution.

Therefore, the only solution to the inequality 3𝑥 + 2𝑦 ≥ 7 is option b) (− 1, 5).

Answer 3

To find a solution to the inequality 3𝑥 + 2𝑦 ≥ 7, we need to check if each of the given options satisfies the inequality. Let's substitute the values for 𝑥 and 𝑦 in each option into the given inequality and see which options satisfy it.

a) For option (0, 0):
Substituting 𝑥 = 0 and 𝑦 = 0 into the inequality, we have:
3(0) + 2(0) ≥ 7
0 ≥ 7

Since 0 is not greater than or equal to 7, option (0, 0) does not satisfy the inequality.

b) For option (−1, 5):
Substituting 𝑥 = −1 and 𝑦 = 5 into the inequality, we have:
3(−1) + 2(5) ≥ 7
−3 + 10 ≥ 7
7 ≥ 7

Since 7 is equal to 7, option (−1, 5) satisfies the inequality.

c) For option (0, −4):
Substituting 𝑥 = 0 and 𝑦 = −4 into the inequality, we have:
3(0) + 2(−4) ≥ 7
0 − 8 ≥ 7
−8 ≥ 7

Since −8 is not greater than or equal to 7, option (0, −4) does not satisfy the inequality.

d) For option (2, 0):
Substituting 𝑥 = 2 and 𝑦 = 0 into the inequality, we have:
3(2) + 2(0) ≥ 7
6 + 0 ≥ 7
6 ≥ 7

Since 6 is not greater than or equal to 7, option (2, 0) does not satisfy the inequality.

Therefore, the solution to the inequality 3𝑥 + 2𝑦 ≥ 7 is option b) (−1, 5).