Which point would be a solution to the system of linear inequalities shown below?
y, is less than, start fraction, 2, divided by, 3, end fraction, x, plus, 1, y, is greater than or equal to, x, minus, 4
y<
3
2
x+1y≥x−4
Answer
Multiple Choice Answers
left bracket, 9, comma, minus, 3, right bracket(9,−3)
left bracket, minus, 9, comma, minus, 9, right bracket(−9,−9)
left bracket, minus, 12, comma, 3, right bracket(−12,3)
left bracket, minus, 12, comma, minus, 2, right bracket(−12,−2)
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.