Answer:
To determine which points lie in the solution set of the system of inequalities x-y>-4, 2x-y<5, and 2y + x>1, we can graph the inequalities on a coordinate plane and look for the region that satisfies all three inequalities.
To graph the inequality x-y>-4, we can first graph the line x-y=-4 by plotting the points on the line:
x y
0 -4
-4 0
Then, we can shade the region above the line, since all points above the line will satisfy the inequality x-y>-4:
|
-4 | x
| /
| /
| /
|/
-8 +------
-4 0
To graph the inequality 2x-y<5, we can first graph the line 2x-y=5 by plotting the points on the line:
x y
0 5
2.5 0
Then, we can shade the region below the line, since all points below the line will satisfy the inequality 2x-y<5:
|
5 | x
| / |
| / |
| / |
|/ |
0 +----|--
0 2.5
To graph the inequality 2y + x>1, we can first graph the line 2y + x = 1 by plotting the points on the line:
x y
0 0.5
1 0
Then, we can shade the region above the line, since all points above the line will satisfy the inequality 2y + x>1:
|
2 | x
| |
1|-----
| /
| /
| /
|/
0 +------
0 1
The solution set of the system of inequalities is the region that satisfies all three inequalities, which is the shaded region in the graph below:
|
5 |
|
| x
2| |
| |
| |
| /|
| / |
0+------+------
-4 0 2.5
So the points that lie in the solution set are:
(-2,3), (-1,3), (2,-2)
Therefore, the correct answers are:
(-2,3), (-1,3), and (2,-2)