Question

Which point would not be a solution to the system of linear inequalities shown below?

y > -1/3x +1 y> x-1
a. ( -3, 7)
b. (9, 9)
c. (-3, 5)
d. (6, -9)

Answer 1

After reviewing the points against the inequalities, point d (6, -9) does not satisfy either inequality, making it the correct answer for the point that would not be a solution to the system of linear inequalities. Option D is the correct answer.

Step-by-step explanation:

The question asks which point would not satisfy the given system of linear inequalities:

• y > -1/3x + 1
• y > x - 1

We need to check which of the given points (-3, 7), (9, 9), (-3, 5), (6, -9) does not satisfy both inequalities.

Checking Each Point:

• For point a (-3, 7):
  y = 7 > -1/3(-3) + 1 = 2 (True)
  y = 7 > -3 - 1 = -4 (True)
• For point b (9, 9):
  y = 9 > -1/3(9) + 1 = 2 (True)
  y = 9 > 9 - 1 = 8 (True)
• For point c (-3, 5):
  y = 5 > -1/3(-3) + 1 = 2 (True)
  y = 5 > -3 - 1 = -4 (True)
• For point d (6, -9):
  y = -9 > -1/3(6) + 1 = -1 (False)
  y = -9 > 6 - 1 = 5 (False)

Conclusively, point d (6, -9) does not satisfy either of the inequalities, making it the correct answer.