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

Question

asked Sep 5, 2022 217k views

1 Answer

Dharmesh Baldha · Answer 1 · 2022-09-09T11:50:49+0000

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.