To determine which point would be a solution to the system of linear inequalities, we can substitute each option into the inequalities and see which one satisfies both of them.
Option 1: (9, -3)
Substituting into the inequalities:
-3 < (2/3)(9) + 1
-3 < 19/3 + 1
-3 < 22/3 (which is true)
-3 ≥ 9 - 4
-3 ≥ 5 (which is false)
Option 2: (-9, -9)
Substituting into the inequalities:
-9 < (2/3)(-9) + 1
-9 < -6/3 + 1
-9 < -4/3 (which is true)
-9 ≥ -9 - 4
-9 ≥ -13 (which is true)
Option 3: (-12, 3)
Substituting into the inequalities:
3 < (2/3)(-12) + 1
3 < -8 + 1 (which is false)
3 ≥ -12 - 4
3 ≥ -16 (which is true)
Option 4: (-12, -2)
Substituting into the inequalities:
-2 < (2/3)(-12) + 1
-2 < -8 + 1 (which is true)
-2 ≥ -12 - 4
-2 ≥ -16 (which is true)
Therefore, the point (-12, -2) would be a solution to the system of linear inequalities.