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)
To determine which of the given points is a solution to the inequality, we can substitute the values of each point into the inequality and check if the inequality is satisfied.
For point (0,0):
3(0) + 2(0) = 0 ≥ 7
This is not true, so (0,0) is not a solution to the inequality.
For point (-1,5):
3(-1) + 2(5) = -3 + 10 = 7 ≥ 7
This is true, so (-1,5) is a solution to the inequality.
For point (0,-4):
3(0) + 2(-4) = 0 - 8 = -8 ≥ 7
This is not true, so (0,-4) is not a solution to the inequality.
For point (2,0):
3(2) + 2(0) = 6 + 0 = 6 ≥ 7
This is not true, so (2,0) is not a solution to the inequality.
Therefore, the only solution to the inequality is (b) (-1,5).
To find the solution to the inequality 3x + 2y ≥ 7, we need to substitute the given values for x and y into the inequality and check if it holds true.
Let's check each option:
a) (0,0)
Substituting x = 0 and y = 0 into the inequality: 3(0) + 2(0) ≥ 7
Simplifying the left side: 0 + 0 ≥ 7
This is not true, so (0,0) is not a solution to the inequality.
b) (-1,5)
Substituting x = -1 and y = 5 into the inequality: 3(-1) + 2(5) ≥ 7
Simplifying the left side: -3 + 10 ≥ 7
This is true, so (-1,5) is a solution to the inequality.
c) (0,-4)
Substituting x = 0 and y = -4 into the inequality: 3(0) + 2(-4) ≥ 7
Simplifying the left side: 0 - 8 ≥ 7
This is not true, so (0,-4) is not a solution to the inequality.
d) (2,0)
Substituting x = 2 and y = 0 into the inequality: 3(2) + 2(0) ≥ 7
Simplifying the left side: 6 + 0 ≥ 7
This is not true, so (2,0) is not a solution to the inequality.
Therefore, the only solution to the inequality 3x + 2y ≥ 7 is (b) (-1,5).
To determine which solution satisfies the inequality 3x + 2y ≥ 7, we can substitute the given values for x and y into the inequality and check if it holds true.
a) (0,0):
3(0) + 2(0) = 0 + 0 = 0 ≥ 7
The inequality is not satisfied.
b) (-1,5):
3(-1) + 2(5) = -3 + 10 = 7 ≥ 7
The inequality is satisfied.
c) (0,-4):
3(0) + 2(-4) = 0 - 8 = -8 ≥ 7
The inequality is not satisfied.
d) (2,0):
3(2) + 2(0) = 6 + 0 = 6 ≥ 7
The inequality is not satisfied.
Therefore, the only solution that satisfies the inequality 3x + 2y ≥ 7 is b) (-1,5).