Answer:
and
Step-by-step explanation:
<u><em>The complete question is</em></u>
Which system of linear inequalities has the point (3,-2) in its solution set?
A.
y < -3
y ≤ 2/3x - 4
B.
y > -3
y ≥ 2/3x - 4
C.
y < -3
y ≥ 2/3x - 4
D.
y > -2
y ≤ 2/3x - 4
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)
<u><em>Verify each case</em></u>
Case A) we have
----> inequality A
----> inequality B
Substitute the value of x and y of the point (3,-2) in both inequalities and then compare the results
Inequality A
----> is not true
therefore
The ordered pair is not a solution of the system A
Case B) we have
----> inequality A
----> inequality B
Substitute the value of x and y of the point (3,-2) in both inequalities and then compare the results
Inequality A
----> is true
Inequality B
----> is true
therefore
The ordered pair is a solution of the system B
Case C) we have
----> inequality A
----> inequality B
Substitute the value of x and y of the point (3,-2) in both inequalities and then compare the results
Inequality A
----> is not true
therefore
The ordered pair is not a solution of the system C
Case D) we have
y > -2 ----> inequality A
----> inequality B
Substitute the value of x and y of the point (3,-2) in both inequalities and then compare the results
Inequality A
----> is not true
therefore
The ordered pair is not a solution of the system D