Answer:
Options (A), (C) and (E)
Explanation:
System of inequalities has ben given as,
y ≥ 0.75x
y ≤ 2x - 7
By satisfying with the points given in the options,
Option A. (8, 8)
y ≥ 0.75x
8 ≥ 0.75(8)
8 ≥ 6
True
y ≤ 2x - 7
8 ≤ 2(8) - 7
8 ≤ 9
True.
Therefore, (8, 8) is the solution of the given system.
Option (B) (2, 2)
y ≥ 0.75x
2 ≥ 0.75(2)
2 ≥ 1.5
True
y ≤ 2x - 7
2 ≤ 2(2) - 7
2 ≤ -3
False
Therefore, Option B is not the solution.
Option C (9, 7)
y ≥ 0.75x
7 ≥ 0.75(9)
7 ≥ 6.75
True
y ≤ 2(x) - 7
7 ≤ 2(9) - 7
7 ≤ 11
True
Therefore, Option B is the solution of the system of inequalities given.
Option D (4, 6)
y ≥ 0.75x
6 ≥ 0.75(4)
6 ≥ 3
True
y ≤ 2x - 7
6 ≤ 2(4) - 7
6 ≤ 1
False
Therefore, Option (D) is not the solution.
Option E (10, 9)
y ≥ 0.75x
9 ≥ 0.75(10)
9 ≥ 7.5
True.
y ≤ 2x - 7
9 ≤ 2(10) - 7
9 ≤ 13
True
Therefore, Option E is the solution of the given system of inequalities.
Options (A), (C) and (E) are the correct options.