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Determine whether the points (–3,–2) and (3,2) are in the solution set of the system of inequalities below. y ≤ ½x + 2 y < –2x – 3

User Worth
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1 Answer

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Given:

The system of inequalities:


y\leq (1)/(2)x+2


y<-2x-3

To find:

Whether the points (–3,–2) and (3,2) are in the solution set of the given system of inequalities.

Solution:

A point is in the solution set of the given system of inequalities if it satisfies both inequalities.

Check for the point (-3,-2).


-2\leq (1)/(2)(-3)+2


-2\leq -1.5+2


-2\leq 0.5

This statement is true.


-2<-2(-3)-3


-2<6-3


-2<3

This statement is also true.

Since the point (-3,-2) satisfies both inequalities, therefore (-3,-2) is in the solution set of the given system of inequalities.

Now, check for the point (3,2).


2<-2(3)-3


2<-6-3


2<-9

This statement is false because
2>-9.

Since the point (3,2) does not satisfy the second inequality, therefore (3,2) is not in the solution set of the given system of inequalities.

User Dharmesh Baldha
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